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  1. (hist) ‎Coversine ‎[680 bytes]
  2. (hist) ‎Pythagorean identity for sin and cos ‎[678 bytes]
  3. (hist) ‎Continued fraction for 2e^(z^2) integral from z to infinity e^(-t^2) dt for positive Re(z) ‎[677 bytes]
  4. (hist) ‎Logarithm of a quotient is a difference of logarithms ‎[676 bytes]
  5. (hist) ‎Logarithm of 1 ‎[675 bytes]
  6. (hist) ‎Legendre P ‎[674 bytes]
  7. (hist) ‎Petr function ‎[673 bytes]
  8. (hist) ‎Derivative of sech ‎[672 bytes]
  9. (hist) ‎Integral of (t-b)^(x-1)(a-t)^(y-1)/(t-x)^(x+y) dt=(a-b)^(x+y-1)/((a-c)^x(b-c)^y) B(x,y) ‎[671 bytes]
  10. (hist) ‎Kelvin functions footer ‎[669 bytes]
  11. (hist) ‎Golden ratio ‎[667 bytes]
  12. (hist) ‎Ratio test ‎[666 bytes]
  13. (hist) ‎Derivative of Jacobi theta 1 at 0 ‎[665 bytes]
  14. (hist) ‎Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 ‎[664 bytes]
  15. (hist) ‎Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 ‎[664 bytes]
  16. (hist) ‎Hankel H (2) in terms of csc and Bessel J ‎[664 bytes]
  17. (hist) ‎Arccosh ‎[661 bytes]
  18. (hist) ‎2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) ‎[659 bytes]
  19. (hist) ‎Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued) ‎[658 bytes]
  20. (hist) ‎Ramanujan tau ‎[658 bytes]
  21. (hist) ‎Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 ‎[654 bytes]
  22. (hist) ‎Paper:Harry Bateman/Some Properties of a certain Set of Polynomials ‎[654 bytes]
  23. (hist) ‎Logarithm base a ‎[653 bytes]
  24. (hist) ‎Hankel H (1) in terms of csc and Bessel J ‎[646 bytes]
  25. (hist) ‎Polylogarithm ‎[646 bytes]
  26. (hist) ‎Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) ‎[645 bytes]
  27. (hist) ‎1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4) ‎[644 bytes]
  28. (hist) ‎Riemann zeta as integral of monomial divided by an exponential ‎[644 bytes]
  29. (hist) ‎Meissel-Mertens constant ‎[644 bytes]
  30. (hist) ‎Derivative of cosh ‎[640 bytes]
  31. (hist) ‎Q-Pochhammer ‎[640 bytes]
  32. (hist) ‎Binomial coefficient (n choose 0) equals 1 ‎[639 bytes]
  33. (hist) ‎Riemann xi ‎[637 bytes]
  34. (hist) ‎E ‎[637 bytes]
  35. (hist) ‎Elliptic K ‎[635 bytes]
  36. (hist) ‎2F0(a,b;;z)2F0(a,b;;-z)=4F1(a,b,a/2+b/2,a/2+b/2+1/2;a+b;4z^2) ‎[634 bytes]
  37. (hist) ‎Exponential integral Ei series ‎[634 bytes]
  38. (hist) ‎Integral representation of Struve function ‎[633 bytes]
  39. (hist) ‎1F1(a;2a;z)1F1(b;2b;-z)=2F3(a/2+b/2,a/2+b/2+1/2;a+1/2,b+1/2,a+b;z^2/4) ‎[633 bytes]
  40. (hist) ‎Derivative of sinh ‎[633 bytes]
  41. (hist) ‎Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! ‎[632 bytes]
  42. (hist) ‎Chi ‎[632 bytes]
  43. (hist) ‎Euler's formula ‎[631 bytes]
  44. (hist) ‎Logarithm (multivalued) of product is a sum of logarithms (multivalued) ‎[629 bytes]
  45. (hist) ‎0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) ‎[626 bytes]
  46. (hist) ‎Error functions footer ‎[624 bytes]
  47. (hist) ‎0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z) ‎[622 bytes]
  48. (hist) ‎Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines ‎[621 bytes]
  49. (hist) ‎Polar coordinates ‎[620 bytes]
  50. (hist) ‎Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 ‎[615 bytes]
  51. (hist) ‎Legendre's constant ‎[615 bytes]
  52. (hist) ‎Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) ‎[612 bytes]
  53. (hist) ‎Riemann function ‎[612 bytes]
  54. (hist) ‎Q-derivative ‎[612 bytes]
  55. (hist) ‎Gamma(1)=1 ‎[606 bytes]
  56. (hist) ‎Paper:James Whitbread Lee Glaisher/On certain definite integrals involving the exponential-integral ‎[605 bytes]
  57. (hist) ‎Logarithm of a quotient of Jacobi theta 4 equals a sum of sines ‎[605 bytes]
  58. (hist) ‎Sum of divisors functions written in terms of partition function ‎[604 bytes]
  59. (hist) ‎Gamma function written as a limit of a factorial, exponential, and a rising factorial ‎[603 bytes]
  60. (hist) ‎Relationship between logarithm (multivalued) and positive integer exponents ‎[603 bytes]
  61. (hist) ‎Spherical Hankel h (2) ‎[603 bytes]
  62. (hist) ‎Spherical Hankel h (1) ‎[603 bytes]
  63. (hist) ‎Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) ‎[600 bytes]
  64. (hist) ‎Prime counting ‎[600 bytes]
  65. (hist) ‎Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 ‎[599 bytes]
  66. (hist) ‎Darboux function ‎[597 bytes]
  67. (hist) ‎Orthogonality of Chebyshev T on (-1,1) ‎[595 bytes]
  68. (hist) ‎Derivative of Li 2(-1/x) ‎[593 bytes]
  69. (hist) ‎Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) ‎[592 bytes]
  70. (hist) ‎Logarithmic derivative of Jacobi theta 4 equals a sum of sines ‎[592 bytes]
  71. (hist) ‎Derivative of arccot ‎[592 bytes]
  72. (hist) ‎Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) ‎[591 bytes]
  73. (hist) ‎Second q-shifted factorial ‎[591 bytes]
  74. (hist) ‎Recurrence relation for Struve fuction ‎[590 bytes]
  75. (hist) ‎Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m ‎[590 bytes]
  76. (hist) ‎Schwarz function ‎[590 bytes]
  77. (hist) ‎Q-calculus footer ‎[590 bytes]
  78. (hist) ‎Scorer Hi ‎[589 bytes]
  79. (hist) ‎Scorer Gi ‎[589 bytes]
  80. (hist) ‎Logarithmic derivative of Jacobi theta 3 equals a sum of sines ‎[588 bytes]
  81. (hist) ‎Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines ‎[588 bytes]
  82. (hist) ‎Series for log(z+a) for positive a and Re(z) greater than -a ‎[587 bytes]
  83. (hist) ‎Reciprocal zeta function ‎[587 bytes]
  84. (hist) ‎Logarithm and friends footer ‎[586 bytes]
  85. (hist) ‎B(x,y)=2^(1-x-y)integral (1+t)^(x-1)(1-t)^(y-1)+(1+t)^(y-1)(1-t)^(x-1) dt ‎[586 bytes]
  86. (hist) ‎Book:Michael Wilensky/Ueber Besselsche Funktionen ‎[583 bytes]
  87. (hist) ‎Reciprocal Fibonacci constant ‎[582 bytes]
  88. (hist) ‎Brun's constant ‎[582 bytes]
  89. (hist) ‎Pure recurrence relation for partition function ‎[581 bytes]
  90. (hist) ‎Polygamma multiplication formula ‎[580 bytes]
  91. (hist) ‎General Dirichlet series ‎[579 bytes]
  92. (hist) ‎Logarithmic derivative of Riemann zeta in terms of series over primes ‎[578 bytes]
  93. (hist) ‎Digamma at 1 ‎[578 bytes]
  94. (hist) ‎Alternating sum over bottom of binomial coefficient with top fixed equals 0 ‎[578 bytes]
  95. (hist) ‎Hurwitz zeta ‎[575 bytes]
  96. (hist) ‎Riemann zeta at even integers ‎[574 bytes]
  97. (hist) ‎Derivative of the logarithm ‎[574 bytes]
  98. (hist) ‎Value of polygamma at 1/2 ‎[574 bytes]
  99. (hist) ‎(z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) ‎[568 bytes]
  100. (hist) ‎Asymptotic behavior of Sievert integral ‎[568 bytes]
  101. (hist) ‎Closed formula for physicist's Hermite polynomials ‎[568 bytes]
  102. (hist) ‎Hypergeometric 1F1 ‎[568 bytes]
  103. (hist) ‎Logarithm of product is a sum of logarithms ‎[567 bytes]
  104. (hist) ‎T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) ‎[566 bytes]
  105. (hist) ‎Integral of (1+t)^(2x-1)(1-t)^(2y-1)(1+t^2)^(-x-y)dt=2^(x+y-2)B(x,y) ‎[566 bytes]
  106. (hist) ‎Dedekind eta ‎[565 bytes]
  107. (hist) ‎H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) ‎[563 bytes]
  108. (hist) ‎Relationship between sinh and sin ‎[563 bytes]
  109. (hist) ‎1/B(n,m)=n((n+m-1) choose (m-1)) ‎[561 bytes]
  110. (hist) ‎1/B(n,m)=m((n+m-1) choose (n-1)) ‎[560 bytes]
  111. (hist) ‎Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 ‎[559 bytes]
  112. (hist) ‎Bessel-Clifford ‎[559 bytes]
  113. (hist) ‎Knopp function ‎[559 bytes]
  114. (hist) ‎Sum of divisors ‎[559 bytes]
  115. (hist) ‎Bernstein B ‎[558 bytes]
  116. (hist) ‎Q-sin sub q ‎[557 bytes]
  117. (hist) ‎Log((1+z)/(1-z)) as continued fraction ‎[556 bytes]
  118. (hist) ‎Elliptic E ‎[556 bytes]
  119. (hist) ‎Taylor series of log(1-z) ‎[555 bytes]
  120. (hist) ‎Genocchi numbers ‎[555 bytes]
  121. (hist) ‎Mertens ‎[555 bytes]
  122. (hist) ‎Binet's formula ‎[551 bytes]
  123. (hist) ‎Exsecant ‎[550 bytes]
  124. (hist) ‎Recurrence relation for Struve function (2) ‎[549 bytes]
  125. (hist) ‎Arccsc ‎[549 bytes]
  126. (hist) ‎E is irrational ‎[548 bytes]
  127. (hist) ‎Riemann Siegel theta function ‎[548 bytes]
  128. (hist) ‎Logarithmic derivative of Riemann zeta in terms of Mangoldt function ‎[546 bytes]
  129. (hist) ‎Digamma functional equation ‎[546 bytes]
  130. (hist) ‎E^x greater than (1+x/y)^y greater than exp(xy/(x+y) for x greater than 0 and y greater than 0) ‎[546 bytes]
  131. (hist) ‎H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) ‎[543 bytes]
  132. (hist) ‎Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 ‎[542 bytes]
  133. (hist) ‎Erfc ‎[542 bytes]
  134. (hist) ‎Relationship between logarithmic integral and exponential integral ‎[542 bytes]
  135. (hist) ‎Generating function for partition function ‎[541 bytes]
  136. (hist) ‎Q-exponential e sub q ‎[541 bytes]
  137. (hist) ‎Series for log(z) for Re(z) greater than 0 ‎[540 bytes]
  138. (hist) ‎2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) ‎[539 bytes]
  139. (hist) ‎Li2(z)=zPhi(z,2,1) ‎[538 bytes]
  140. (hist) ‎Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) ‎[538 bytes]
  141. (hist) ‎Dickson polynomial ‎[538 bytes]
  142. (hist) ‎B(x,y)B(x+y,z)B(x+y+z,u)=Gamma(x)Gamma(y)Gamma(z)Gamma(u)/Gamma(x+y+z+u) ‎[537 bytes]
  143. (hist) ‎Functional equation for Riemann zeta ‎[536 bytes]
  144. (hist) ‎Product representation of q-exponential E sub 1/q ‎[535 bytes]
  145. (hist) ‎Value of polygamma at positive integer ‎[534 bytes]
  146. (hist) ‎Asymptotic formula for partition function ‎[533 bytes]
  147. (hist) ‎Series for log(riemann zeta) over primes ‎[532 bytes]
  148. (hist) ‎Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4 ‎[531 bytes]
  149. (hist) ‎Chebyshev theta function ‎[531 bytes]
  150. (hist) ‎U n(x)=Sum (-1)^k n!/((2k+1)!(n-2k-1)!)(1-x^2)^(k+1/2)x^(n-2k-1) ‎[530 bytes]
  151. (hist) ‎Recurrence relation for partition function with sum of divisors ‎[530 bytes]
  152. (hist) ‎Modular form ‎[528 bytes]
  153. (hist) ‎Quotient rule for derivatives ‎[526 bytes]
  154. (hist) ‎Faber F1 ‎[526 bytes]
  155. (hist) ‎Arcsec ‎[526 bytes]
  156. (hist) ‎U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n ‎[525 bytes]
  157. (hist) ‎Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications ‎[525 bytes]
  158. (hist) ‎D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) ‎[525 bytes]
  159. (hist) ‎Dirichlet function ‎[525 bytes]
  160. (hist) ‎Two-sided inequality for e^(x^2) integral from x to infinity e^(-t^2) dt for non-negative real x ‎[524 bytes]
  161. (hist) ‎Digamma at n+1/2 ‎[523 bytes]
  162. (hist) ‎Faber F2 ‎[523 bytes]
  163. (hist) ‎Euler numbers ‎[522 bytes]
  164. (hist) ‎Integral of Bessel J for nu=2n ‎[522 bytes]
  165. (hist) ‎Clausen cosine ‎[521 bytes]
  166. (hist) ‎Derivative of Gudermannian ‎[521 bytes]
  167. (hist) ‎Constant multiple rule for derivatives ‎[519 bytes]
  168. (hist) ‎Euler E generating function ‎[519 bytes]
  169. (hist) ‎Bernoulli B ‎[519 bytes]
  170. (hist) ‎Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 ‎[518 bytes]
  171. (hist) ‎E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0 ‎[518 bytes]
  172. (hist) ‎Paper:Lucas Jódar/On the hypergeometric matrix function ‎[517 bytes]
  173. (hist) ‎(c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 ‎[517 bytes]
  174. (hist) ‎Beta as improper integral ‎[517 bytes]
  175. (hist) ‎Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) ‎[516 bytes]
  176. (hist) ‎Log(1+z) as continued fraction ‎[516 bytes]
  177. (hist) ‎C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 ‎[516 bytes]
  178. (hist) ‎Sum over bottom of binomial coefficient with top fixed equals 2^n ‎[516 bytes]
  179. (hist) ‎Z coth(z) = 2z/(e^(2z)-1) + z ‎[515 bytes]
  180. (hist) ‎Series for log(Riemann zeta) in terms of Mangoldt function ‎[515 bytes]
  181. (hist) ‎E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 ‎[515 bytes]
  182. (hist) ‎Q-zeta ‎[514 bytes]
  183. (hist) ‎Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1 ‎[513 bytes]
  184. (hist) ‎Q-cos sub q ‎[513 bytes]
  185. (hist) ‎1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 ‎[512 bytes]
  186. (hist) ‎(c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 ‎[511 bytes]
  187. (hist) ‎Bernoulli numbers ‎[511 bytes]
  188. (hist) ‎Halving identity for tangent (2) ‎[510 bytes]
  189. (hist) ‎Halving identity for tangent (3) ‎[508 bytes]
  190. (hist) ‎Functional equation for Riemann zeta with cosine ‎[508 bytes]
  191. (hist) ‎Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x) ‎[508 bytes]
  192. (hist) ‎Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1 ‎[506 bytes]
  193. (hist) ‎(b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 ‎[505 bytes]
  194. (hist) ‎Integral of Bessel J for Re(nu) greater than -1 ‎[505 bytes]
  195. (hist) ‎2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z ‎[505 bytes]
  196. (hist) ‎Jacobi cd ‎[505 bytes]
  197. (hist) ‎Jacobi ds ‎[505 bytes]
  198. (hist) ‎Jacobi sc ‎[505 bytes]
  199. (hist) ‎Laplace cdf ‎[499 bytes]
  200. (hist) ‎2F1(1/2,1;3/2;-z^2)=arctan(z)/z ‎[499 bytes]
  201. (hist) ‎Q-Gaussian distribution ‎[498 bytes]
  202. (hist) ‎Q-Cos ‎[498 bytes]
  203. (hist) ‎Generating function for Hermite (physicist) polynomials ‎[497 bytes]
  204. (hist) ‎Inverse error function ‎[496 bytes]
  205. (hist) ‎2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) ‎[495 bytes]
  206. (hist) ‎Sum of totient equals z/((1-z) squared) ‎[495 bytes]
  207. (hist) ‎Book:Sir Thomas L. Heath/Euclid: The Thirteen Books of The Elements: Volume 2/Second Edition ‎[495 bytes]
  208. (hist) ‎Polygamma reflection formula ‎[495 bytes]
  209. (hist) ‎Relationship between Weber function and Anger function ‎[494 bytes]
  210. (hist) ‎1Phi0(a;;z) as infinite product ‎[493 bytes]
  211. (hist) ‎Product representation of totient ‎[493 bytes]
  212. (hist) ‎Chain rule for derivatives ‎[493 bytes]
  213. (hist) ‎McCarthy function ‎[493 bytes]
  214. (hist) ‎Jacobi dc ‎[493 bytes]
  215. (hist) ‎Jacobi cs ‎[493 bytes]
  216. (hist) ‎Jacobi sd ‎[493 bytes]
  217. (hist) ‎Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1 ‎[491 bytes]
  218. (hist) ‎Orthogonality of Gegenbauer C on (-1,1) ‎[490 bytes]
  219. (hist) ‎Continuous ‎[490 bytes]
  220. (hist) ‎Integral of Bessel J for nu=n+1 ‎[489 bytes]
  221. (hist) ‎Logarithm (multivalued) of the exponential ‎[489 bytes]
  222. (hist) ‎Series for log(z) for Re(z) greater than 1/2 ‎[489 bytes]
  223. (hist) ‎Dirichlet beta ‎[489 bytes]
  224. (hist) ‎Real and imaginary parts of log ‎[488 bytes]
  225. (hist) ‎Integral representation of polygamma for Re(z) greater than 0 ‎[488 bytes]
  226. (hist) ‎Q-Hurwitz zeta ‎[487 bytes]
  227. (hist) ‎Identity written as a sum of Möbius functions ‎[487 bytes]
  228. (hist) ‎Logarithm diverges to negative infinity at 0 from right ‎[487 bytes]
  229. (hist) ‎X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 ‎[486 bytes]
  230. (hist) ‎D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) ‎[484 bytes]
  231. (hist) ‎1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) ‎[483 bytes]
  232. (hist) ‎Pochhammer symbol with non-negative integer subscript ‎[483 bytes]
  233. (hist) ‎Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) ‎[482 bytes]
  234. (hist) ‎Q-difference equation for q-exponential E sub 1/q ‎[482 bytes]
  235. (hist) ‎Value of polygamma at 1 ‎[482 bytes]
  236. (hist) ‎E(1,1)(z)=exp(z) ‎[481 bytes]
  237. (hist) ‎2F1(1,1;2;z)=-log(1-z)/z ‎[481 bytes]
  238. (hist) ‎Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 ‎[481 bytes]
  239. (hist) ‎Contour integral representation of reciprocal gamma ‎[480 bytes]
  240. (hist) ‎Spherical Bessel j ‎[480 bytes]
  241. (hist) ‎E(2,1)(-z^2)=cos(z) ‎[479 bytes]
  242. (hist) ‎Jinc ‎[479 bytes]
  243. (hist) ‎Q-Sin ‎[479 bytes]
  244. (hist) ‎E(2,1)(z)=cosh(sqrt(z)) ‎[478 bytes]
  245. (hist) ‎H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 ‎[478 bytes]
  246. (hist) ‎Pythagorean identity for tanh and sech ‎[478 bytes]
  247. (hist) ‎Faddeeva function ‎[478 bytes]
  248. (hist) ‎B(x,y)B(x+y,z)=B(z,x)B(x+z,y) ‎[476 bytes]
  249. (hist) ‎X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 ‎[476 bytes]
  250. (hist) ‎Beta as product of gamma functions ‎[475 bytes]
  251. (hist) ‎Bessel at n+1/2 in terms of Bessel polynomial ‎[475 bytes]
  252. (hist) ‎Limit of log(x)/x^a=0 ‎[474 bytes]
  253. (hist) ‎Euler phi ‎[474 bytes]
  254. (hist) ‎Generating relation for Bateman F ‎[473 bytes]
  255. (hist) ‎Value of derivative of trigamma at positive integer plus 1/2 ‎[473 bytes]
  256. (hist) ‎Weierstrass nowhere differentiable function ‎[473 bytes]
  257. (hist) ‎(c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0 ‎[472 bytes]
  258. (hist) ‎Integral of Bessel J for nu=2n+1 ‎[472 bytes]
  259. (hist) ‎Digamma at z+n ‎[472 bytes]
  260. (hist) ‎Taylor series of log(1+z) ‎[472 bytes]
  261. (hist) ‎Clausen sine ‎[471 bytes]
  262. (hist) ‎Series for log(z) for absolute value of (z-1) less than 1 ‎[471 bytes]
  263. (hist) ‎Sum of cosh and sinh ‎[470 bytes]
  264. (hist) ‎Orthogonality of Laguerre L ‎[469 bytes]
  265. (hist) ‎F(-n)=(-1)^(n+1)F(n) ‎[469 bytes]
  266. (hist) ‎Airy zeta function ‎[468 bytes]
  267. (hist) ‎Relationship between sine, imaginary number, logarithm, and the golden ratio ‎[467 bytes]
  268. (hist) ‎Spherical Bessel y ‎[466 bytes]
  269. (hist) ‎E^x is less than 1/(1-x) for nonzero real x less than 1 ‎[465 bytes]
  270. (hist) ‎H (-(n+1/2))(z)=(-1)^n J (n+1/2)(z) for integer n geq 0 ‎[464 bytes]
  271. (hist) ‎(c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0 ‎[464 bytes]
  272. (hist) ‎Period of tanh ‎[464 bytes]
  273. (hist) ‎Polygamma recurrence relation ‎[464 bytes]
  274. (hist) ‎Weierstrass elementary factors ‎[464 bytes]
  275. (hist) ‎Bessel polynomial ‎[464 bytes]
  276. (hist) ‎Halving identity for tangent (1) ‎[462 bytes]
  277. (hist) ‎Gauss' formula for gamma function ‎[462 bytes]
  278. (hist) ‎Riemann-Siegel Z ‎[462 bytes]
  279. (hist) ‎K-function ‎[461 bytes]
  280. (hist) ‎Digamma at 1/2 ‎[461 bytes]
  281. (hist) ‎B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt ‎[460 bytes]
  282. (hist) ‎Paper:V.E. Hoggatt, Jr/Triangular numbers ‎[460 bytes]
  283. (hist) ‎Series for polygamma in terms of Riemann zeta ‎[459 bytes]
  284. (hist) ‎Antiderivative of the logarithm ‎[458 bytes]
  285. (hist) ‎Floor ‎[457 bytes]
  286. (hist) ‎T n(x)=(1/2)(x+i sqrt(1-x^2))^n+(1/2)(x-i sqrt(1-x^2))^n ‎[456 bytes]
  287. (hist) ‎Pythagorean identity for coth and csch ‎[456 bytes]
  288. (hist) ‎Period of sinh ‎[456 bytes]
  289. (hist) ‎Sqrt(1-z^2)2F1(1,1;3/2;z^2)=arcsin(z)/z ‎[456 bytes]
  290. (hist) ‎E^x is greater than 1+x for nonzero real x ‎[456 bytes]
  291. (hist) ‎Relationship between Anger function and Weber function ‎[456 bytes]
  292. (hist) ‎Relationship between Bessel J sub n and Bessel J sub -n ‎[455 bytes]
  293. (hist) ‎Catalan's constant ‎[455 bytes]
  294. (hist) ‎Hypergeometric 2F3 ‎[454 bytes]
  295. (hist) ‎Limit of q-exponential E sub 1/q for 0 less than q less than 1 ‎[454 bytes]
  296. (hist) ‎Relationship between Li 2(1),Li 2(-1), and pi ‎[454 bytes]
  297. (hist) ‎Glyphs ‎[454 bytes]
  298. (hist) ‎E(m)=(pi/2)2F1(-1/2,1/2;1;m) ‎[453 bytes]
  299. (hist) ‎Buchstab function ‎[453 bytes]
  300. (hist) ‎K(m)=(pi/2)2F1(1/2,1/2;1;m) ‎[452 bytes]
  301. (hist) ‎Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z)) ‎[452 bytes]
  302. (hist) ‎Q-derivative of q-Cosine ‎[450 bytes]
  303. (hist) ‎Reciprocal Riemann zeta in terms of Mobius ‎[449 bytes]
  304. (hist) ‎Jacobi ns ‎[449 bytes]
  305. (hist) ‎Arccsch ‎[449 bytes]
  306. (hist) ‎Limit of quotient of consecutive Fibonacci numbers ‎[448 bytes]
  307. (hist) ‎Paper:D.S. McAnally/q-exponential and q-gamma functions. I. q-exponential functions ‎[447 bytes]
  308. (hist) ‎Q-difference equation for q-exponential E sub q ‎[447 bytes]
  309. (hist) ‎Generating function for Laguerre L ‎[444 bytes]
  310. (hist) ‎Normal cdf ‎[444 bytes]
  311. (hist) ‎Unit step function ‎[444 bytes]
  312. (hist) ‎Two-dimensional Laplace transform ‎[444 bytes]
  313. (hist) ‎Jacobi nd ‎[444 bytes]
  314. (hist) ‎Relationship between Struve function and hypergeometric pFq ‎[443 bytes]
  315. (hist) ‎Orthogonality of Bateman F on R ‎[442 bytes]
  316. (hist) ‎Integral of (z^n)log(z)dz=(z^(n+1)/(n+1))log(z)-z^(n+1)/(n+1)^2 for integer n neq -1 ‎[442 bytes]
  317. (hist) ‎Product rule for derivatives ‎[442 bytes]
  318. (hist) ‎Jackson q-Bessel (1) ‎[442 bytes]
  319. (hist) ‎Halving identity for sinh ‎[441 bytes]
  320. (hist) ‎Jackson q-Bessel (2) ‎[441 bytes]
  321. (hist) ‎Artin-Mazur zeta function ‎[441 bytes]
  322. (hist) ‎Period of cosh ‎[440 bytes]
  323. (hist) ‎Greatest prime factor ‎[440 bytes]
  324. (hist) ‎Q-derivative of q-Sine ‎[439 bytes]
  325. (hist) ‎Doubling identity for sinh (2) ‎[438 bytes]
  326. (hist) ‎Taylor series ‎[438 bytes]
  327. (hist) ‎L(n)^2-5F(n)^2=4(-1)^n ‎[437 bytes]
  328. (hist) ‎Dawson D+ ‎[437 bytes]
  329. (hist) ‎Legendre chi ‎[436 bytes]
  330. (hist) ‎Weierstrass elliptic ‎[435 bytes]
  331. (hist) ‎Matrix exponential ‎[434 bytes]
  332. (hist) ‎Difference of cosh and sinh ‎[434 bytes]
  333. (hist) ‎B(x,y+1)=(y/x)B(x+1,y) ‎[434 bytes]
  334. (hist) ‎Relationship between csch and csc ‎[434 bytes]
  335. (hist) ‎Symmetry relation of exponential integral E ‎[433 bytes]
  336. (hist) ‎E (0,1)(z)=1/(1-z) for abs(z) less than 1 ‎[432 bytes]
  337. (hist) ‎Log(x) less than or equal to n(x^(1/n)-1) ‎[432 bytes]
  338. (hist) ‎Stirling numbers of the second kind ‎[432 bytes]
  339. (hist) ‎Jacobi nc ‎[432 bytes]
  340. (hist) ‎Hypergeometric 2F0 ‎[431 bytes]
  341. (hist) ‎Sum rule for derivatives ‎[431 bytes]
  342. (hist) ‎Absolute convergence of secant zeta function ‎[430 bytes]
  343. (hist) ‎Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k) ‎[430 bytes]
  344. (hist) ‎Relationship between Scorer Hi and Airy functions ‎[430 bytes]
  345. (hist) ‎Lower incomplete gamma ‎[430 bytes]
  346. (hist) ‎Orthogonality relation for cosine on (0,pi) ‎[429 bytes]
  347. (hist) ‎B(x,y)B(x+y,z)=B(y,z)B(y+z,x) ‎[428 bytes]
  348. (hist) ‎Relationship between sech and sec ‎[428 bytes]
  349. (hist) ‎B(x,y+1)=(y/(x+y))B(x,y) ‎[427 bytes]
  350. (hist) ‎E is limit of (1+1/n)^n ‎[427 bytes]
  351. (hist) ‎Logarithm at minus 1 ‎[427 bytes]
  352. (hist) ‎Relationship between Legendre polynomial and hypergeometric 2F1 ‎[426 bytes]
  353. (hist) ‎Hyperfactorial ‎[426 bytes]
  354. (hist) ‎Doubling identity for sinh (1) ‎[425 bytes]
  355. (hist) ‎Limit of x^a log(x)=0 ‎[425 bytes]
  356. (hist) ‎Fresnel C in terms of erf ‎[425 bytes]
  357. (hist) ‎Fresnel S in terms of erf ‎[425 bytes]
  358. (hist) ‎Minkowski question mark ‎[425 bytes]
  359. (hist) ‎E^(-x/(1-x)) is less than 1-x is less than e^(-x) for nonzero real x less than 1 ‎[424 bytes]
  360. (hist) ‎Paper:Edmund Landau/Sur la série des inverse de nombres de Fibonacci ‎[423 bytes]
  361. (hist) ‎Relationship between the Gegenbauer C polynomials and the Jacobi P polynomials ‎[423 bytes]
  362. (hist) ‎L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) ‎[422 bytes]
  363. (hist) ‎Cosh of a sum ‎[422 bytes]
  364. (hist) ‎L(n)=F(n+1)+F(n-1) ‎[422 bytes]
  365. (hist) ‎Beta in terms of gamma ‎[422 bytes]
  366. (hist) ‎Derivative of Struve H0 ‎[421 bytes]
  367. (hist) ‎Log 10(z)=log 10(e)log(z) ‎[421 bytes]
  368. (hist) ‎Relationship between Bessel Y sub n and Bessel Y sub -n ‎[421 bytes]
  369. (hist) ‎Relationship between Scorer Gi and Airy functions ‎[421 bytes]
  370. (hist) ‎Fibonacci polynomial ‎[421 bytes]
  371. (hist) ‎Doubling identity for cosh (2) ‎[419 bytes]
  372. (hist) ‎Dirichlet series ‎[418 bytes]
  373. (hist) ‎Meromorphic continuation of q-exponential E sub q ‎[418 bytes]
  374. (hist) ‎Chebyshev psi function ‎[418 bytes]
  375. (hist) ‎F(2n)=F(n)L(n) ‎[417 bytes]
  376. (hist) ‎Lagrange polynomial ‎[417 bytes]
  377. (hist) ‎Arcsin cdf ‎[416 bytes]
  378. (hist) ‎Sinh of a sum ‎[416 bytes]
  379. (hist) ‎Differential equation for Jacobi P ‎[416 bytes]
  380. (hist) ‎Halving identity for cosh ‎[414 bytes]
  381. (hist) ‎Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1)) ‎[414 bytes]
  382. (hist) ‎Logarithm of exponential ‎[413 bytes]
  383. (hist) ‎Erfi ‎[413 bytes]
  384. (hist) ‎Relationship between Airy Bi and modified Bessel I ‎[413 bytes]
  385. (hist) ‎Arcsech ‎[413 bytes]
  386. (hist) ‎Hypergeometric 4F1 ‎[412 bytes]
  387. (hist) ‎Loggamma ‎[412 bytes]
  388. (hist) ‎Period parallelogram ‎[411 bytes]
  389. (hist) ‎Klein invariant J ‎[411 bytes]
  390. (hist) ‎Series for q-sin sub q ‎[408 bytes]
  391. (hist) ‎Rodrigues formula for Meixner polynomial ‎[408 bytes]
  392. (hist) ‎Derivative ‎[408 bytes]
  393. (hist) ‎Abs(log(1+z)) less than or equal to -log(1-abs(z)) ‎[407 bytes]
  394. (hist) ‎Relationship between tanh and tan ‎[406 bytes]
  395. (hist) ‎Bessel at -n-1/2 in terms of Bessel polynomial ‎[406 bytes]
  396. (hist) ‎Li 2(1)=pi^2/6 ‎[404 bytes]
  397. (hist) ‎Doubling identity for cosh (3) ‎[403 bytes]
  398. (hist) ‎Riemann-Landau xi ‎[403 bytes]
  399. (hist) ‎Logarithm at i ‎[403 bytes]
  400. (hist) ‎Abs(log(1-x)) less than 3x/2 ‎[402 bytes]
  401. (hist) ‎F(n+m+1)=F(n+1)F(m+1)+F(n)F(m) ‎[402 bytes]
  402. (hist) ‎Normal pdf ‎[401 bytes]
  403. (hist) ‎Euler E n'(x)=nE n-1(x) ‎[401 bytes]
  404. (hist) ‎Hypergeometric 3F2 ‎[401 bytes]
  405. (hist) ‎Sum of squares of Fibonacci numbers ‎[401 bytes]
  406. (hist) ‎Haversine ‎[401 bytes]
  407. (hist) ‎Relationship between cosh and cos ‎[401 bytes]
  408. (hist) ‎Coth of a sum ‎[400 bytes]
  409. (hist) ‎Log(z)=log(10)log 10(z) ‎[400 bytes]
  410. (hist) ‎Distance to integers ‎[400 bytes]
  411. (hist) ‎Relationship between coth and cot ‎[400 bytes]
  412. (hist) ‎Relationship between Bessel J and hypergeometric 0F1 ‎[400 bytes]
  413. (hist) ‎Log 10(z)=log(z)/log(10) ‎[399 bytes]
  414. (hist) ‎Log e(z)=log(z) ‎[399 bytes]
  415. (hist) ‎Recurrence relation of exponential integral E ‎[399 bytes]
  416. (hist) ‎Relationship between logarithm and positive integer exponents ‎[397 bytes]
  417. (hist) ‎Partial derivative of beta function ‎[397 bytes]
  418. (hist) ‎Tanh of a sum ‎[396 bytes]
  419. (hist) ‎Erf of conjugate is conjugate of erf ‎[396 bytes]
  420. (hist) ‎Q-Gamma at z+1 ‎[396 bytes]
  421. (hist) ‎Neumann polynomial ‎[396 bytes]
  422. (hist) ‎Catalan's constant using Hurwitz zeta ‎[396 bytes]
  423. (hist) ‎Meissel-Mertens constant in terms of the Euler-Mascheroni constant ‎[395 bytes]
  424. (hist) ‎Bessel polynomial generalized hypergeometric ‎[394 bytes]
  425. (hist) ‎Cauchy cdf ‎[393 bytes]
  426. (hist) ‎Orthogonality of Chebyshev U on (-1,1) ‎[392 bytes]
  427. (hist) ‎Q-number when a=n is a natural number ‎[392 bytes]
  428. (hist) ‎Hypergeometric 1F2 ‎[391 bytes]
  429. (hist) ‎Relationship between spherical Bessel j and sine ‎[391 bytes]
  430. (hist) ‎Identity ‎[390 bytes]
  431. (hist) ‎Sum of Lucas numbers ‎[389 bytes]
  432. (hist) ‎Anger of integer order is Bessel J ‎[389 bytes]
  433. (hist) ‎Q-derivative power rule ‎[388 bytes]
  434. (hist) ‎Paper:Maruti Ram Murty/The Fibonacci Zeta Function ‎[387 bytes]
  435. (hist) ‎Relationship between spherical Bessel y and cosine ‎[387 bytes]
  436. (hist) ‎Bell polynomial ‎[386 bytes]
  437. (hist) ‎Logarithm at -i ‎[385 bytes]
  438. (hist) ‎Nth derivative of logarithm ‎[384 bytes]
  439. (hist) ‎Trigamma ‎[384 bytes]
  440. (hist) ‎-log(1-x) less than x/(1-x) ‎[381 bytes]
  441. (hist) ‎T(n)^2=T(T(n))+T(T(n)-1) ‎[381 bytes]
  442. (hist) ‎Falling factorial ‎[380 bytes]
  443. (hist) ‎Sum of Fibonacci numbers ‎[379 bytes]
  444. (hist) ‎Ramanujan theta function ‎[379 bytes]
  445. (hist) ‎Dirichlet L-function ‎[379 bytes]
  446. (hist) ‎Matrix e^A=limit of (I+A/s)^s ‎[377 bytes]
  447. (hist) ‎Log(x) less than or equal to x-1 ‎[377 bytes]
  448. (hist) ‎Binomial coefficient (n choose n) equals 1 ‎[377 bytes]
  449. (hist) ‎Relationship between Chebyshev T and Gegenbauer C ‎[377 bytes]
  450. (hist) ‎Erdős-Borwein Constant ‎[377 bytes]
  451. (hist) ‎Lerch zeta function ‎[376 bytes]
  452. (hist) ‎Doubling identity for cosh (1) ‎[374 bytes]
  453. (hist) ‎Lattice generated by doubly periodic periods ‎[374 bytes]
  454. (hist) ‎N^2=T(n)+T(n-1) ‎[373 bytes]
  455. (hist) ‎Relationship between cosine, imaginary number, logarithm, and the golden ratio ‎[373 bytes]
  456. (hist) ‎Log a(b)=1/log b(a) ‎[372 bytes]
  457. (hist) ‎T(n+1)^2-T(n)^2=(n+1)^3 ‎[372 bytes]
  458. (hist) ‎Binomial coefficient (n choose k) equals (n choose (n-k)) ‎[371 bytes]
  459. (hist) ‎Hypergeometric 0F3 ‎[370 bytes]
  460. (hist) ‎Complex number ‎[370 bytes]
  461. (hist) ‎Antiderivative of inverse error function ‎[369 bytes]
  462. (hist) ‎Q-Polygamma function ‎[368 bytes]
  463. (hist) ‎X less than -log(1-x) ‎[367 bytes]
  464. (hist) ‎(n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x) ‎[366 bytes]
  465. (hist) ‎Reciprocal of i ‎[366 bytes]
  466. (hist) ‎T(n+1)=T(n)+n+1 ‎[365 bytes]
  467. (hist) ‎L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1) ‎[365 bytes]
  468. (hist) ‎Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm ‎[365 bytes]
  469. (hist) ‎Paper:Matilde Lalín/Secant zeta functions ‎[365 bytes]
  470. (hist) ‎Relationship between sin and sinh ‎[365 bytes]
  471. (hist) ‎Bessel polynomial in terms of Bessel functions ‎[365 bytes]
  472. (hist) ‎Derivative of inverse error function ‎[364 bytes]
  473. (hist) ‎Exponential of logarithm ‎[364 bytes]
  474. (hist) ‎Tetrahedral numbers ‎[364 bytes]
  475. (hist) ‎Antiderivative of hyperbolic cosecant ‎[364 bytes]
  476. (hist) ‎X/(1+x) less than log(1+x) ‎[363 bytes]
  477. (hist) ‎Integral of log of inverse erf from 0 to 1 ‎[363 bytes]
  478. (hist) ‎F(2n+1)=F(n+1)^2+F(n)^2 ‎[362 bytes]
  479. (hist) ‎2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t) ‎[361 bytes]
  480. (hist) ‎Wallis product ‎[361 bytes]
  481. (hist) ‎Paper:Yilmaz Simsek/q-Dedekind type sums related to q-zeta function and basic L-series ‎[360 bytes]
  482. (hist) ‎Log base a in terms of logarithm base b ‎[359 bytes]
  483. (hist) ‎Gamma(n+1)=n! ‎[359 bytes]
  484. (hist) ‎Cellérier function ‎[359 bytes]
  485. (hist) ‎Sister Celine's polynomials ‎[359 bytes]
  486. (hist) ‎Relationship between Airy Ai and modified Bessel K ‎[359 bytes]
  487. (hist) ‎Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta ‎[359 bytes]
  488. (hist) ‎F(2n)=F(n+1)^2-F(n-1)^2 ‎[358 bytes]
  489. (hist) ‎Q-Euler formula for E sub q ‎[358 bytes]
  490. (hist) ‎F(n+1)F(n-1)-F(n)^2=(-1)^n ‎[357 bytes]
  491. (hist) ‎XL n'(x)=nL n(x)-n L (n-1)(x) ‎[356 bytes]
  492. (hist) ‎Shi ‎[356 bytes]
  493. (hist) ‎Gamma recurrence relation ‎[355 bytes]
  494. (hist) ‎Logarithm of a complex number ‎[353 bytes]
  495. (hist) ‎Continuous uniform cdf ‎[351 bytes]
  496. (hist) ‎Paper:Daniel S. Moak/The q-gamma function for q greater than 1 ‎[351 bytes]
  497. (hist) ‎Cauchy pdf ‎[350 bytes]
  498. (hist) ‎Log(1+x) less than x ‎[350 bytes]
  499. (hist) ‎Arcsin as inverse sine ‎[349 bytes]
  500. (hist) ‎L n'(x)=-Sum L k(x) ‎[348 bytes]

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