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  1. (hist) ‎Main Page ‎[26,335 bytes]
  2. (hist) ‎Book:Milton Abramowitz/Handbook of mathematical functions ‎[22,945 bytes]
  3. (hist) ‎Book:Harris Hancock/Lectures on the theory of elliptic functions ‎[21,675 bytes]
  4. (hist) ‎Full list ‎[11,824 bytes]
  5. (hist) ‎Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus ‎[10,895 bytes]
  6. (hist) ‎Book:Arthur Erdélyi/Higher Transcendental Functions Volume I ‎[10,131 bytes]
  7. (hist) ‎Format notes ‎[8,372 bytes]
  8. (hist) ‎Book:Earl David Rainville/Special Functions ‎[7,600 bytes]
  9. (hist) ‎Book:Nicholas Higham/Functions of Matrices: Theory and Computation ‎[7,340 bytes]
  10. (hist) ‎Book:Larry C. Andrews/Special Functions of Mathematics for Engineers ‎[7,229 bytes]
  11. (hist) ‎Book:Roelof Koekoek/Hypergeometric Orthogonal Polynomials and Their q-Analogues ‎[6,583 bytes]
  12. (hist) ‎Book:George E. Andrews/Special Functions ‎[6,451 bytes]
  13. (hist) ‎Book:Arthur Erdélyi/Higher Transcendental Functions Volume II ‎[5,461 bytes]
  14. (hist) ‎Book:Arthur Erdélyi/Higher Transcendental Functions Volume III ‎[5,424 bytes]
  15. (hist) ‎Integral representation of Airy Ai ‎[5,219 bytes]
  16. (hist) ‎Gamma ‎[4,956 bytes]
  17. (hist) ‎Book:W.W. Bell/Special Functions for Scientists and Engineers ‎[4,907 bytes]
  18. (hist) ‎Book:Aleksandar Ivić/The Riemann Zeta-Function ‎[4,774 bytes]
  19. (hist) ‎Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition ‎[4,613 bytes]
  20. (hist) ‎Book:Leonard Lewin/Polylogarithms and Associated Functions/Second Edition ‎[4,563 bytes]
  21. (hist) ‎Book:Richard Beals/Special functions, a graduate text ‎[3,713 bytes]
  22. (hist) ‎Book:Leonard Lewin/Dilogarithms and Associated Functions ‎[3,621 bytes]
  23. (hist) ‎Laplace transform ‎[3,604 bytes]
  24. (hist) ‎Beta ‎[3,351 bytes]
  25. (hist) ‎Bessel J ‎[3,343 bytes]
  26. (hist) ‎Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition ‎[3,339 bytes]
  27. (hist) ‎Differential equation for Hypergeometric pFq ‎[3,221 bytes]
  28. (hist) ‎Derivatives of Hypergeometric pFq ‎[3,035 bytes]
  29. (hist) ‎Riemann zeta ‎[2,961 bytes]
  30. (hist) ‎Logarithm ‎[2,947 bytes]
  31. (hist) ‎Hypergeometric 2F1 ‎[2,913 bytes]
  32. (hist) ‎Book:George Eyre Andrews/Number Theory ‎[2,819 bytes]
  33. (hist) ‎Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry ‎[2,710 bytes]
  34. (hist) ‎Polygonal numbers footer ‎[2,454 bytes]
  35. (hist) ‎Orthogonal polynomials footer ‎[2,454 bytes]
  36. (hist) ‎Euler totient ‎[2,406 bytes]
  37. (hist) ‎Fibonacci numbers ‎[2,393 bytes]
  38. (hist) ‎Book:T.S. Chihara/An Introduction to Orthogonal Polynomials ‎[2,255 bytes]
  39. (hist) ‎Fibonacci zeta in terms of a sum of binomial coefficients ‎[2,229 bytes]
  40. (hist) ‎Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I ‎[2,215 bytes]
  41. (hist) ‎Book:Elena Deza/Figurate Numbers ‎[2,176 bytes]
  42. (hist) ‎Binomial theorem ‎[2,127 bytes]
  43. (hist) ‎Convergence of Hypergeometric pFq ‎[2,119 bytes]
  44. (hist) ‎Elliptic function ‎[2,074 bytes]
  45. (hist) ‎Jacobi elliptic functions footer ‎[2,068 bytes]
  46. (hist) ‎Prime zeta P ‎[2,062 bytes]
  47. (hist) ‎Dilogarithm ‎[1,977 bytes]
  48. (hist) ‎Number theory functions footer ‎[1,972 bytes]
  49. (hist) ‎Hypergeometric pFq ‎[1,972 bytes]
  50. (hist) ‎Hadamard gamma ‎[1,960 bytes]
  51. (hist) ‎Exponential ‎[1,949 bytes]
  52. (hist) ‎Error function ‎[1,946 bytes]
  53. (hist) ‎Q-Gamma ‎[1,889 bytes]
  54. (hist) ‎Book:Charalambos Charalambides/Discrete q-Distributions ‎[1,888 bytes]
  55. (hist) ‎Binomial coefficient ‎[1,869 bytes]
  56. (hist) ‎Hermite (physicist) ‎[1,845 bytes]
  57. (hist) ‎The Euler-Mascheroni constant exists ‎[1,824 bytes]
  58. (hist) ‎Möbius ‎[1,821 bytes]
  59. (hist) ‎Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition ‎[1,771 bytes]
  60. (hist) ‎Book:Andrew Gray/A Treatise on Bessel Functions ‎[1,689 bytes]
  61. (hist) ‎Polygamma ‎[1,674 bytes]
  62. (hist) ‎Sinh ‎[1,656 bytes]
  63. (hist) ‎Hermite (probabilist) ‎[1,656 bytes]
  64. (hist) ‎Book:Victor Kac/Quantum Calculus ‎[1,636 bytes]
  65. (hist) ‎Euler-Mascheroni constant ‎[1,619 bytes]
  66. (hist) ‎Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition ‎[1,603 bytes]
  67. (hist) ‎Sine ‎[1,593 bytes]
  68. (hist) ‎Airy Bi ‎[1,589 bytes]
  69. (hist) ‎*-integral functions footer ‎[1,575 bytes]
  70. (hist) ‎Cosh ‎[1,568 bytes]
  71. (hist) ‎Airy Ai ‎[1,548 bytes]
  72. (hist) ‎Struve function ‎[1,535 bytes]
  73. (hist) ‎Arcsin ‎[1,533 bytes]
  74. (hist) ‎Book:Johann Heinrich Graf/Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale ‎[1,526 bytes]
  75. (hist) ‎Bolzano function ‎[1,499 bytes]
  76. (hist) ‎Pochhammer ‎[1,490 bytes]
  77. (hist) ‎Pi ‎[1,477 bytes]
  78. (hist) ‎Beta in terms of sine and cosine ‎[1,474 bytes]
  79. (hist) ‎Bessel functions footer ‎[1,464 bytes]
  80. (hist) ‎Anger function ‎[1,397 bytes]
  81. (hist) ‎Exponential integral E ‎[1,391 bytes]
  82. (hist) ‎Meixner polynomial ‎[1,364 bytes]
  83. (hist) ‎Jacobi theta 2 ‎[1,362 bytes]
  84. (hist) ‎Integral of Bessel J for nu=1 ‎[1,361 bytes]
  85. (hist) ‎Jacobi theta 4 ‎[1,349 bytes]
  86. (hist) ‎Coth ‎[1,341 bytes]
  87. (hist) ‎Q-Binomial ‎[1,332 bytes]
  88. (hist) ‎Cosine ‎[1,308 bytes]
  89. (hist) ‎Tanh ‎[1,304 bytes]
  90. (hist) ‎Jacobi theta 3 ‎[1,298 bytes]
  91. (hist) ‎Jacobi theta 1 ‎[1,278 bytes]
  92. (hist) ‎Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann ‎[1,267 bytes]
  93. (hist) ‎Taylor series of cosine ‎[1,259 bytes]
  94. (hist) ‎Taylor series of sine ‎[1,228 bytes]
  95. (hist) ‎Book:Richard Dedekind/Essays on the Theory of Numbers ‎[1,221 bytes]
  96. (hist) ‎Q-number ‎[1,215 bytes]
  97. (hist) ‎Book:Johan Thim/Continuous Nowhere Differentiable Functions ‎[1,202 bytes]
  98. (hist) ‎Continuous q-Hermite polynomial ‎[1,198 bytes]
  99. (hist) ‎Sinc ‎[1,179 bytes]
  100. (hist) ‎Mott polynomial ‎[1,176 bytes]
  101. (hist) ‎Gegenbauer C ‎[1,166 bytes]
  102. (hist) ‎Exponential integral Ei ‎[1,156 bytes]
  103. (hist) ‎Closed form for partition function with sinh ‎[1,155 bytes]
  104. (hist) ‎Thomae function ‎[1,147 bytes]
  105. (hist) ‎Csch ‎[1,138 bytes]
  106. (hist) ‎Reciprocal gamma written as an infinite product ‎[1,133 bytes]
  107. (hist) ‎Beta in terms of power of t over power of (1+t) ‎[1,116 bytes]
  108. (hist) ‎Bessel Y ‎[1,116 bytes]
  109. (hist) ‎Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions ‎[1,101 bytes]
  110. (hist) ‎Taylor series for error function ‎[1,095 bytes]
  111. (hist) ‎Cosecant ‎[1,090 bytes]
  112. (hist) ‎Laguerre L ‎[1,090 bytes]
  113. (hist) ‎Sech ‎[1,084 bytes]
  114. (hist) ‎Arakawa-Kaneko zeta function ‎[1,082 bytes]
  115. (hist) ‎Bateman F ‎[1,079 bytes]
  116. (hist) ‎Generalized q-Bessel ‎[1,076 bytes]
  117. (hist) ‎Devil's staircase ‎[1,070 bytes]
  118. (hist) ‎Liouville lambda ‎[1,051 bytes]
  119. (hist) ‎Derivative of prime zeta ‎[1,047 bytes]
  120. (hist) ‎Logarithm (multivalued) ‎[1,047 bytes]
  121. (hist) ‎Antiderivative of arctan ‎[1,043 bytes]
  122. (hist) ‎Chebyshev T ‎[1,016 bytes]
  123. (hist) ‎Sine integral ‎[1,012 bytes]
  124. (hist) ‎Derivative of cosine ‎[1,007 bytes]
  125. (hist) ‎Kelvin ber ‎[1,001 bytes]
  126. (hist) ‎Signum ‎[999 bytes]
  127. (hist) ‎Q-shifted factorial ‎[997 bytes]
  128. (hist) ‎Derivative of arcsinh ‎[995 bytes]
  129. (hist) ‎Logarithmic integral ‎[994 bytes]
  130. (hist) ‎Q-factorial ‎[994 bytes]
  131. (hist) ‎Hypergeometric functions footer ‎[987 bytes]
  132. (hist) ‎Derivative of sine ‎[980 bytes]
  133. (hist) ‎Relationship between logarithm (multivalued) and logarithm ‎[975 bytes]
  134. (hist) ‎Lambert W ‎[974 bytes]
  135. (hist) ‎Cotangent ‎[970 bytes]
  136. (hist) ‎Inverse hyperbolic trigonometric functions footer ‎[967 bytes]
  137. (hist) ‎Digamma ‎[967 bytes]
  138. (hist) ‎Inverse Gudermannian ‎[966 bytes]
  139. (hist) ‎Derivative of cotangent ‎[963 bytes]
  140. (hist) ‎Derivative of arcsec ‎[955 bytes]
  141. (hist) ‎Modified Bessel I ‎[954 bytes]
  142. (hist) ‎Hankel H (1) ‎[953 bytes]
  143. (hist) ‎Inverse trigonometric functions footer ‎[949 bytes]
  144. (hist) ‎Q-exponential E sub q ‎[946 bytes]
  145. (hist) ‎Gamma(z+1)=zGamma(z) ‎[930 bytes]
  146. (hist) ‎Continuous nowhere differentiable functions footer ‎[925 bytes]
  147. (hist) ‎Trigonometric functions footer ‎[924 bytes]
  148. (hist) ‎Weierstrass factorization theorem ‎[923 bytes]
  149. (hist) ‎Arccos ‎[916 bytes]
  150. (hist) ‎Tangent ‎[916 bytes]
  151. (hist) ‎Relationship between dilogarithm and log(1-z)/z ‎[912 bytes]
  152. (hist) ‎Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt ‎[910 bytes]
  153. (hist) ‎Book:F.E. Relton/Applied Bessel Functions ‎[908 bytes]
  154. (hist) ‎Kelvin bei ‎[902 bytes]
  155. (hist) ‎Gudermannian ‎[901 bytes]
  156. (hist) ‎Book:W.N. Bailey/Generalized Hypergeometric Series ‎[898 bytes]
  157. (hist) ‎Hyperbolic trigonometric functions footer ‎[897 bytes]
  158. (hist) ‎Antiderivative of arccos ‎[896 bytes]
  159. (hist) ‎Dedekind zeta function ‎[896 bytes]
  160. (hist) ‎Reciprocal gamma ‎[893 bytes]
  161. (hist) ‎Ceiling ‎[887 bytes]
  162. (hist) ‎Fresnel C ‎[871 bytes]
  163. (hist) ‎Derivative of tangent ‎[870 bytes]
  164. (hist) ‎Fresnel S ‎[867 bytes]
  165. (hist) ‎*-c functions footer ‎[866 bytes]
  166. (hist) ‎Difference equation of hypergeometric type ‎[862 bytes]
  167. (hist) ‎Cosine integral ‎[860 bytes]
  168. (hist) ‎Z2F1(1,1;2,-z) equals log(1+z) ‎[853 bytes]
  169. (hist) ‎Depreciated trigonometric functions footer ‎[849 bytes]
  170. (hist) ‎Product of Weierstrass elementary factors is entire ‎[845 bytes]
  171. (hist) ‎Derivative of arcsin ‎[845 bytes]
  172. (hist) ‎Associated Laguerre L ‎[845 bytes]
  173. (hist) ‎Book:Alfred George Greenhill/The applications of elliptic functions ‎[841 bytes]
  174. (hist) ‎Barnes G ‎[838 bytes]
  175. (hist) ‎Relationship between Sievert integral and exponential integral E ‎[835 bytes]
  176. (hist) ‎Ei(x)=-Integral from -x to infinity of e^(-t)/t dt ‎[829 bytes]
  177. (hist) ‎Derivative of coth ‎[829 bytes]
  178. (hist) ‎Hankel functions footer ‎[827 bytes]
  179. (hist) ‎Jacobi P ‎[826 bytes]
  180. (hist) ‎Derivative of tanh ‎[824 bytes]
  181. (hist) ‎Partition ‎[820 bytes]
  182. (hist) ‎Book:G.H. Hardy/The General Theory Of Dirichlet's Series ‎[819 bytes]
  183. (hist) ‎Jacobi sn ‎[815 bytes]
  184. (hist) ‎Secant ‎[814 bytes]
  185. (hist) ‎Integral representation of Struve function (3) ‎[813 bytes]
  186. (hist) ‎Kelvin ker ‎[811 bytes]
  187. (hist) ‎Hypergeometric 0F1 ‎[809 bytes]
  188. (hist) ‎Hankel H (2) ‎[809 bytes]
  189. (hist) ‎Derivative of the exponential function ‎[806 bytes]
  190. (hist) ‎Charlier polynomial ‎[801 bytes]
  191. (hist) ‎Error function is odd ‎[800 bytes]
  192. (hist) ‎Basic hypergeometric series psi ‎[798 bytes]
  193. (hist) ‎Logarithm of quotient of Jacobi theta 2 equals the log of a quotient of cosines + a sum of sines ‎[794 bytes]
  194. (hist) ‎Jacobi dn ‎[794 bytes]
  195. (hist) ‎Arcsinh ‎[792 bytes]
  196. (hist) ‎Gamma function written as infinite product ‎[791 bytes]
  197. (hist) ‎Basic hypergeometric phi ‎[786 bytes]
  198. (hist) ‎Hahn polynomial ‎[784 bytes]
  199. (hist) ‎Weber function ‎[781 bytes]
  200. (hist) ‎Chebyshev U ‎[778 bytes]
  201. (hist) ‎Arctan ‎[778 bytes]
  202. (hist) ‎Modified Bessel K ‎[775 bytes]
  203. (hist) ‎Derivative of Bessel Y with respect to its order ‎[774 bytes]
  204. (hist) ‎Q-Fibonacci polynomials ‎[773 bytes]
  205. (hist) ‎Pythagorean identity for sinh and cosh ‎[772 bytes]
  206. (hist) ‎Mangoldt ‎[770 bytes]
  207. (hist) ‎Lucas numbers ‎[769 bytes]
  208. (hist) ‎Antiderivative of coth ‎[769 bytes]
  209. (hist) ‎Beta is symmetric ‎[765 bytes]
  210. (hist) ‎Ihara zeta function ‎[765 bytes]
  211. (hist) ‎Riemann zeta as contour integral ‎[764 bytes]
  212. (hist) ‎Q-Bessel functions ‎[764 bytes]
  213. (hist) ‎Jacobi cn ‎[762 bytes]
  214. (hist) ‎Integral of monomial times Bessel J ‎[760 bytes]
  215. (hist) ‎Derivative of secant ‎[755 bytes]
  216. (hist) ‎Euler E ‎[754 bytes]
  217. (hist) ‎Mittag-Leffler ‎[752 bytes]
  218. (hist) ‎Kelvin kei ‎[749 bytes]
  219. (hist) ‎Book:Bernard Dwork/Generalized hypergeometric functions ‎[742 bytes]
  220. (hist) ‎Takagi function ‎[740 bytes]
  221. (hist) ‎Derivative of cosecant ‎[740 bytes]
  222. (hist) ‎Derivative of arccos ‎[736 bytes]
  223. (hist) ‎Relationship between arctan and arccot ‎[735 bytes]
  224. (hist) ‎Versine ‎[734 bytes]
  225. (hist) ‎Logarithm of quotient of Jacobi theta 1 equals the log of a quotient of sines + a sum of sines ‎[731 bytes]
  226. (hist) ‎Airy functions footer ‎[729 bytes]
  227. (hist) ‎Q-exponential E sub 1/q ‎[728 bytes]
  228. (hist) ‎Euler product for Riemann zeta ‎[727 bytes]
  229. (hist) ‎Van der Waerden function ‎[726 bytes]
  230. (hist) ‎Antiderivative of tanh ‎[725 bytes]
  231. (hist) ‎Arccoth ‎[722 bytes]
  232. (hist) ‎Dirichlet beta in terms of Lerch transcendent ‎[720 bytes]
  233. (hist) ‎Digamma at n+1 ‎[720 bytes]
  234. (hist) ‎Derivative of arctan ‎[720 bytes]
  235. (hist) ‎Jacobi theta footer ‎[718 bytes]
  236. (hist) ‎Arctanh ‎[718 bytes]
  237. (hist) ‎Integral of (1+bt^z)^(-y)t^x dt = (1/z)*b^(-(x+1)/z) B((x+1)/z,y-(x+1)/z) ‎[717 bytes]
  238. (hist) ‎Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I ‎[717 bytes]
  239. (hist) ‎Logarithm of quotient of Jacobi theta 3 equals a sum of sines ‎[707 bytes]
  240. (hist) ‎Fibonacci zeta function ‎[704 bytes]
  241. (hist) ‎Triangular numbers ‎[702 bytes]
  242. (hist) ‎Integral representation of Struve function (2) ‎[699 bytes]
  243. (hist) ‎Derivative of hyperbolic cosecant ‎[696 bytes]
  244. (hist) ‎Sievert integral ‎[692 bytes]
  245. (hist) ‎Integral of (t-b)^(x-1)(a-t)^(y-1)/(c-t)^(x+y) dt = (a-b)^(x+y-1)/((c-a)^x (c-b)^y) B(x,y) ‎[688 bytes]
  246. (hist) ‎Catalan's constant using Legendre chi ‎[687 bytes]
  247. (hist) ‎Derivative of Bessel J with respect to its order ‎[685 bytes]
  248. (hist) ‎Arccot ‎[685 bytes]
  249. (hist) ‎Lerch transcendent ‎[685 bytes]
  250. (hist) ‎Apéry's constant ‎[682 bytes]
  251. (hist) ‎Coversine ‎[680 bytes]
  252. (hist) ‎Pythagorean identity for sin and cos ‎[678 bytes]
  253. (hist) ‎Continued fraction for 2e^(z^2) integral from z to infinity e^(-t^2) dt for positive Re(z) ‎[677 bytes]
  254. (hist) ‎Logarithm of a quotient is a difference of logarithms ‎[676 bytes]
  255. (hist) ‎Logarithm of 1 ‎[675 bytes]
  256. (hist) ‎Legendre P ‎[674 bytes]
  257. (hist) ‎Petr function ‎[673 bytes]
  258. (hist) ‎Derivative of sech ‎[672 bytes]
  259. (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]
  260. (hist) ‎Kelvin functions footer ‎[669 bytes]
  261. (hist) ‎Golden ratio ‎[667 bytes]
  262. (hist) ‎Ratio test ‎[666 bytes]
  263. (hist) ‎Derivative of Jacobi theta 1 at 0 ‎[665 bytes]
  264. (hist) ‎Squares of theta relation for Jacobi theta 3 and Jacobi theta 4 ‎[664 bytes]
  265. (hist) ‎Squares of theta relation for Jacobi theta 2 and Jacobi theta 4 ‎[664 bytes]
  266. (hist) ‎Hankel H (2) in terms of csc and Bessel J ‎[664 bytes]
  267. (hist) ‎Arccosh ‎[661 bytes]
  268. (hist) ‎2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z) ‎[659 bytes]
  269. (hist) ‎Logarithm (multivalued) of a quotient is a difference of logarithms (multivalued) ‎[658 bytes]
  270. (hist) ‎Ramanujan tau ‎[658 bytes]
  271. (hist) ‎Squares of theta relation for Jacobi theta 4 and Jacobi theta 4 ‎[654 bytes]
  272. (hist) ‎Paper:Harry Bateman/Some Properties of a certain Set of Polynomials ‎[654 bytes]
  273. (hist) ‎Logarithm base a ‎[653 bytes]
  274. (hist) ‎Hankel H (1) in terms of csc and Bessel J ‎[646 bytes]
  275. (hist) ‎Polylogarithm ‎[646 bytes]
  276. (hist) ‎Integral of t^(x-1)(1-t^z)^(y-1) dt=(1/z)B(x/z,y) ‎[645 bytes]
  277. (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]
  278. (hist) ‎Riemann zeta as integral of monomial divided by an exponential ‎[644 bytes]
  279. (hist) ‎Meissel-Mertens constant ‎[644 bytes]
  280. (hist) ‎Derivative of cosh ‎[640 bytes]
  281. (hist) ‎Q-Pochhammer ‎[640 bytes]
  282. (hist) ‎Binomial coefficient (n choose 0) equals 1 ‎[639 bytes]
  283. (hist) ‎Riemann xi ‎[637 bytes]
  284. (hist) ‎E ‎[637 bytes]
  285. (hist) ‎Elliptic K ‎[635 bytes]
  286. (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]
  287. (hist) ‎Exponential integral Ei series ‎[634 bytes]
  288. (hist) ‎Integral representation of Struve function ‎[633 bytes]
  289. (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]
  290. (hist) ‎Derivative of sinh ‎[633 bytes]
  291. (hist) ‎Z coth(z) = sum of 2^(2n)B (2n) z^(2n)/(2n)! ‎[632 bytes]
  292. (hist) ‎Chi ‎[632 bytes]
  293. (hist) ‎Euler's formula ‎[631 bytes]
  294. (hist) ‎Logarithm (multivalued) of product is a sum of logarithms (multivalued) ‎[629 bytes]
  295. (hist) ‎0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4) ‎[626 bytes]
  296. (hist) ‎Error functions footer ‎[624 bytes]
  297. (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]
  298. (hist) ‎Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines ‎[621 bytes]
  299. (hist) ‎Polar coordinates ‎[620 bytes]
  300. (hist) ‎Squares of theta relation for Jacobi theta 1 and Jacobi theta 4 ‎[615 bytes]
  301. (hist) ‎Legendre's constant ‎[615 bytes]
  302. (hist) ‎Integral (t-b)^(x-1)(a-t)^(y-1)dt=(a-b)^(x+y-1)B(x,y) ‎[612 bytes]
  303. (hist) ‎Riemann function ‎[612 bytes]
  304. (hist) ‎Q-derivative ‎[612 bytes]
  305. (hist) ‎Gamma(1)=1 ‎[606 bytes]
  306. (hist) ‎Paper:James Whitbread Lee Glaisher/On certain definite integrals involving the exponential-integral ‎[605 bytes]
  307. (hist) ‎Logarithm of a quotient of Jacobi theta 4 equals a sum of sines ‎[605 bytes]
  308. (hist) ‎Sum of divisors functions written in terms of partition function ‎[604 bytes]
  309. (hist) ‎Gamma function written as a limit of a factorial, exponential, and a rising factorial ‎[603 bytes]
  310. (hist) ‎Relationship between logarithm (multivalued) and positive integer exponents ‎[603 bytes]
  311. (hist) ‎Spherical Hankel h (2) ‎[603 bytes]
  312. (hist) ‎Spherical Hankel h (1) ‎[603 bytes]
  313. (hist) ‎Integral t^(x-1)(1-t)^(y-1)(1+bt)^(-x-y)dt = (1+b)^(-x)B(x,y) ‎[600 bytes]
  314. (hist) ‎Prime counting ‎[600 bytes]
  315. (hist) ‎Li 2(z)=-Li 2(1/z)-(1/2)(log z)^2 + i pi log(z) + pi^2/3 ‎[599 bytes]
  316. (hist) ‎Darboux function ‎[597 bytes]
  317. (hist) ‎Orthogonality of Chebyshev T on (-1,1) ‎[595 bytes]
  318. (hist) ‎Derivative of Li 2(-1/x) ‎[593 bytes]
  319. (hist) ‎Z coth(z) = 2 Sum of (-1)^(n+1) zeta(2n) z^(2n)/pi^(2n) ‎[592 bytes]
  320. (hist) ‎Logarithmic derivative of Jacobi theta 4 equals a sum of sines ‎[592 bytes]
  321. (hist) ‎Derivative of arccot ‎[592 bytes]
  322. (hist) ‎Integral t^(x-1)(1+bt)^(-x-y) dt = b^(-x) B(x,y) ‎[591 bytes]
  323. (hist) ‎Second q-shifted factorial ‎[591 bytes]
  324. (hist) ‎Recurrence relation for Struve fuction ‎[590 bytes]
  325. (hist) ‎Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m ‎[590 bytes]
  326. (hist) ‎Schwarz function ‎[590 bytes]
  327. (hist) ‎Q-calculus footer ‎[590 bytes]
  328. (hist) ‎Scorer Hi ‎[589 bytes]
  329. (hist) ‎Scorer Gi ‎[589 bytes]
  330. (hist) ‎Logarithmic derivative of Jacobi theta 3 equals a sum of sines ‎[588 bytes]
  331. (hist) ‎Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines ‎[588 bytes]
  332. (hist) ‎Series for log(z+a) for positive a and Re(z) greater than -a ‎[587 bytes]
  333. (hist) ‎Reciprocal zeta function ‎[587 bytes]
  334. (hist) ‎Logarithm and friends footer ‎[586 bytes]
  335. (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]
  336. (hist) ‎Book:Michael Wilensky/Ueber Besselsche Funktionen ‎[583 bytes]
  337. (hist) ‎Reciprocal Fibonacci constant ‎[582 bytes]
  338. (hist) ‎Brun's constant ‎[582 bytes]
  339. (hist) ‎Pure recurrence relation for partition function ‎[581 bytes]
  340. (hist) ‎Polygamma multiplication formula ‎[580 bytes]
  341. (hist) ‎General Dirichlet series ‎[579 bytes]
  342. (hist) ‎Logarithmic derivative of Riemann zeta in terms of series over primes ‎[578 bytes]
  343. (hist) ‎Digamma at 1 ‎[578 bytes]
  344. (hist) ‎Alternating sum over bottom of binomial coefficient with top fixed equals 0 ‎[578 bytes]
  345. (hist) ‎Hurwitz zeta ‎[575 bytes]
  346. (hist) ‎Riemann zeta at even integers ‎[574 bytes]
  347. (hist) ‎Derivative of the logarithm ‎[574 bytes]
  348. (hist) ‎Value of polygamma at 1/2 ‎[574 bytes]
  349. (hist) ‎(z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k) ‎[568 bytes]
  350. (hist) ‎Asymptotic behavior of Sievert integral ‎[568 bytes]
  351. (hist) ‎Closed formula for physicist's Hermite polynomials ‎[568 bytes]
  352. (hist) ‎Hypergeometric 1F1 ‎[568 bytes]
  353. (hist) ‎Logarithm of product is a sum of logarithms ‎[567 bytes]
  354. (hist) ‎T n(x)=Sum (-1)^k n!/((2k)! (n-2k)!) (1-x^2)^k x^(n-2k) ‎[566 bytes]
  355. (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]
  356. (hist) ‎Dedekind eta ‎[565 bytes]
  357. (hist) ‎H (3/2)(z)=sqrt(z/(2pi))(1+2/z^2)-sqrt(2/(pi z))(sin(z)+cos(z)/z) ‎[563 bytes]
  358. (hist) ‎Relationship between sinh and sin ‎[563 bytes]
  359. (hist) ‎1/B(n,m)=n((n+m-1) choose (m-1)) ‎[561 bytes]
  360. (hist) ‎1/B(n,m)=m((n+m-1) choose (n-1)) ‎[560 bytes]
  361. (hist) ‎Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0 ‎[559 bytes]
  362. (hist) ‎Bessel-Clifford ‎[559 bytes]
  363. (hist) ‎Knopp function ‎[559 bytes]
  364. (hist) ‎Sum of divisors ‎[559 bytes]
  365. (hist) ‎Bernstein B ‎[558 bytes]
  366. (hist) ‎Q-sin sub q ‎[557 bytes]
  367. (hist) ‎Log((1+z)/(1-z)) as continued fraction ‎[556 bytes]
  368. (hist) ‎Elliptic E ‎[556 bytes]
  369. (hist) ‎Taylor series of log(1-z) ‎[555 bytes]
  370. (hist) ‎Genocchi numbers ‎[555 bytes]
  371. (hist) ‎Mertens ‎[555 bytes]
  372. (hist) ‎Binet's formula ‎[551 bytes]
  373. (hist) ‎Exsecant ‎[550 bytes]
  374. (hist) ‎Recurrence relation for Struve function (2) ‎[549 bytes]
  375. (hist) ‎Arccsc ‎[549 bytes]
  376. (hist) ‎E is irrational ‎[548 bytes]
  377. (hist) ‎Riemann Siegel theta function ‎[548 bytes]
  378. (hist) ‎Logarithmic derivative of Riemann zeta in terms of Mangoldt function ‎[546 bytes]
  379. (hist) ‎Digamma functional equation ‎[546 bytes]
  380. (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]
  381. (hist) ‎H (1/2)(z)=sqrt(2/(pi z))(1-cos(z)) ‎[543 bytes]
  382. (hist) ‎Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3 ‎[542 bytes]
  383. (hist) ‎Erfc ‎[542 bytes]
  384. (hist) ‎Relationship between logarithmic integral and exponential integral ‎[542 bytes]
  385. (hist) ‎Generating function for partition function ‎[541 bytes]
  386. (hist) ‎Q-exponential e sub q ‎[541 bytes]
  387. (hist) ‎Series for log(z) for Re(z) greater than 0 ‎[540 bytes]
  388. (hist) ‎2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k) ‎[539 bytes]
  389. (hist) ‎Li2(z)=zPhi(z,2,1) ‎[538 bytes]
  390. (hist) ‎Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2)) ‎[538 bytes]
  391. (hist) ‎Dickson polynomial ‎[538 bytes]
  392. (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]
  393. (hist) ‎Functional equation for Riemann zeta ‎[536 bytes]
  394. (hist) ‎Product representation of q-exponential E sub 1/q ‎[535 bytes]
  395. (hist) ‎Value of polygamma at positive integer ‎[534 bytes]
  396. (hist) ‎Asymptotic formula for partition function ‎[533 bytes]
  397. (hist) ‎Series for log(riemann zeta) over primes ‎[532 bytes]
  398. (hist) ‎Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4 ‎[531 bytes]
  399. (hist) ‎Chebyshev theta function ‎[531 bytes]
  400. (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]
  401. (hist) ‎Recurrence relation for partition function with sum of divisors ‎[530 bytes]
  402. (hist) ‎Modular form ‎[528 bytes]
  403. (hist) ‎Quotient rule for derivatives ‎[526 bytes]
  404. (hist) ‎Faber F1 ‎[526 bytes]
  405. (hist) ‎Arcsec ‎[526 bytes]
  406. (hist) ‎U n(x)=(-i/2)(x+i sqrt(1-x^2))^n+(-i/2)(x-i sqrt(1-x^2))^n ‎[525 bytes]
  407. (hist) ‎Paper:H.J. Haubold/Mittag-Leffler Functions and Their Applications ‎[525 bytes]
  408. (hist) ‎D/dz(z^(-nu)H (nu))=1/(sqrt(pi)2^(nu)Gamma(nu+3/2))-z^(-nu)H (nu+1) ‎[525 bytes]
  409. (hist) ‎Dirichlet function ‎[525 bytes]
  410. (hist) ‎Two-sided inequality for e^(x^2) integral from x to infinity e^(-t^2) dt for non-negative real x ‎[524 bytes]
  411. (hist) ‎Digamma at n+1/2 ‎[523 bytes]
  412. (hist) ‎Faber F2 ‎[523 bytes]
  413. (hist) ‎Euler numbers ‎[522 bytes]
  414. (hist) ‎Integral of Bessel J for nu=2n ‎[522 bytes]
  415. (hist) ‎Clausen cosine ‎[521 bytes]
  416. (hist) ‎Derivative of Gudermannian ‎[521 bytes]
  417. (hist) ‎Constant multiple rule for derivatives ‎[519 bytes]
  418. (hist) ‎Euler E generating function ‎[519 bytes]
  419. (hist) ‎Bernoulli B ‎[519 bytes]
  420. (hist) ‎Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2 ‎[518 bytes]
  421. (hist) ‎E^x greater than 1+x^n/n! for n greater than 0 and nonzero real x greater than 0 ‎[518 bytes]
  422. (hist) ‎Paper:Lucas Jódar/On the hypergeometric matrix function ‎[517 bytes]
  423. (hist) ‎(c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0 ‎[517 bytes]
  424. (hist) ‎Beta as improper integral ‎[517 bytes]
  425. (hist) ‎Li 2(z)+Li 2(1-z)=pi^2/6-log(z)log(1-z) ‎[516 bytes]
  426. (hist) ‎Log(1+z) as continued fraction ‎[516 bytes]
  427. (hist) ‎C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0 ‎[516 bytes]
  428. (hist) ‎Sum over bottom of binomial coefficient with top fixed equals 2^n ‎[516 bytes]
  429. (hist) ‎Z coth(z) = 2z/(e^(2z)-1) + z ‎[515 bytes]
  430. (hist) ‎Series for log(Riemann zeta) in terms of Mangoldt function ‎[515 bytes]
  431. (hist) ‎E^(-x) less than 1-(x/2) for 0 less than x less than or equal to 1.5936 ‎[515 bytes]
  432. (hist) ‎Q-zeta ‎[514 bytes]
  433. (hist) ‎Laurent series for log((z+1)/(z-1)) for absolute value of z greater than 1 ‎[513 bytes]
  434. (hist) ‎Q-cos sub q ‎[513 bytes]
  435. (hist) ‎1+x greater than exp(x/(1+x)) for nonzero real x greater than -1 ‎[512 bytes]
  436. (hist) ‎(c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0 ‎[511 bytes]
  437. (hist) ‎Bernoulli numbers ‎[511 bytes]
  438. (hist) ‎Halving identity for tangent (2) ‎[510 bytes]
  439. (hist) ‎Halving identity for tangent (3) ‎[508 bytes]
  440. (hist) ‎Functional equation for Riemann zeta with cosine ‎[508 bytes]
  441. (hist) ‎Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x) ‎[508 bytes]
  442. (hist) ‎Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1 ‎[506 bytes]
  443. (hist) ‎(b-a)2F1+a2F1(a+1)-b2F1(b+1)=0 ‎[505 bytes]
  444. (hist) ‎Integral of Bessel J for Re(nu) greater than -1 ‎[505 bytes]
  445. (hist) ‎2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z ‎[505 bytes]
  446. (hist) ‎Jacobi cd ‎[505 bytes]
  447. (hist) ‎Jacobi ds ‎[505 bytes]
  448. (hist) ‎Jacobi sc ‎[505 bytes]
  449. (hist) ‎Laplace cdf ‎[499 bytes]
  450. (hist) ‎2F1(1/2,1;3/2;-z^2)=arctan(z)/z ‎[499 bytes]
  451. (hist) ‎Q-Gaussian distribution ‎[498 bytes]
  452. (hist) ‎Q-Cos ‎[498 bytes]
  453. (hist) ‎Generating function for Hermite (physicist) polynomials ‎[497 bytes]
  454. (hist) ‎Inverse error function ‎[496 bytes]
  455. (hist) ‎2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z) ‎[495 bytes]
  456. (hist) ‎Sum of totient equals z/((1-z) squared) ‎[495 bytes]
  457. (hist) ‎Book:Sir Thomas L. Heath/Euclid: The Thirteen Books of The Elements: Volume 2/Second Edition ‎[495 bytes]
  458. (hist) ‎Polygamma reflection formula ‎[495 bytes]
  459. (hist) ‎Relationship between Weber function and Anger function ‎[494 bytes]
  460. (hist) ‎1Phi0(a;;z) as infinite product ‎[493 bytes]
  461. (hist) ‎Product representation of totient ‎[493 bytes]
  462. (hist) ‎Chain rule for derivatives ‎[493 bytes]
  463. (hist) ‎McCarthy function ‎[493 bytes]
  464. (hist) ‎Jacobi dc ‎[493 bytes]
  465. (hist) ‎Jacobi cs ‎[493 bytes]
  466. (hist) ‎Jacobi sd ‎[493 bytes]
  467. (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]
  468. (hist) ‎Orthogonality of Gegenbauer C on (-1,1) ‎[490 bytes]
  469. (hist) ‎Continuous ‎[490 bytes]
  470. (hist) ‎Integral of Bessel J for nu=n+1 ‎[489 bytes]
  471. (hist) ‎Logarithm (multivalued) of the exponential ‎[489 bytes]
  472. (hist) ‎Series for log(z) for Re(z) greater than 1/2 ‎[489 bytes]
  473. (hist) ‎Dirichlet beta ‎[489 bytes]
  474. (hist) ‎Real and imaginary parts of log ‎[488 bytes]
  475. (hist) ‎Integral representation of polygamma for Re(z) greater than 0 ‎[488 bytes]
  476. (hist) ‎Q-Hurwitz zeta ‎[487 bytes]
  477. (hist) ‎Identity written as a sum of Möbius functions ‎[487 bytes]
  478. (hist) ‎Logarithm diverges to negative infinity at 0 from right ‎[487 bytes]
  479. (hist) ‎X less than e^x-1 less than x/(1-x) for nonzero real x less than 1 ‎[486 bytes]
  480. (hist) ‎D/dz(z^(nu)H (nu))=z^(nu)H (nu-1) ‎[484 bytes]
  481. (hist) ‎1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z) ‎[483 bytes]
  482. (hist) ‎Pochhammer symbol with non-negative integer subscript ‎[483 bytes]
  483. (hist) ‎Gamma'(z)/Gamma(z)=-gamma-1/z+Sum z/(k(z+k)) ‎[482 bytes]
  484. (hist) ‎Q-difference equation for q-exponential E sub 1/q ‎[482 bytes]
  485. (hist) ‎Value of polygamma at 1 ‎[482 bytes]
  486. (hist) ‎E(1,1)(z)=exp(z) ‎[481 bytes]
  487. (hist) ‎2F1(1,1;2;z)=-log(1-z)/z ‎[481 bytes]
  488. (hist) ‎Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1 ‎[481 bytes]
  489. (hist) ‎Contour integral representation of reciprocal gamma ‎[480 bytes]
  490. (hist) ‎Spherical Bessel j ‎[480 bytes]
  491. (hist) ‎E(2,1)(-z^2)=cos(z) ‎[479 bytes]
  492. (hist) ‎Jinc ‎[479 bytes]
  493. (hist) ‎Q-Sin ‎[479 bytes]
  494. (hist) ‎E(2,1)(z)=cosh(sqrt(z)) ‎[478 bytes]
  495. (hist) ‎H (nu)(x) geq 0 for x gt 0 and nu geq 1/2 ‎[478 bytes]
  496. (hist) ‎Pythagorean identity for tanh and sech ‎[478 bytes]
  497. (hist) ‎Faddeeva function ‎[478 bytes]
  498. (hist) ‎B(x,y)B(x+y,z)=B(z,x)B(x+z,y) ‎[476 bytes]
  499. (hist) ‎X/(1+x) less than 1-e^(-x) less than x for nonzero real x greater than -1 ‎[476 bytes]
  500. (hist) ‎Beta as product of gamma functions ‎[475 bytes]

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