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  1. (b-a)2F1+a2F1(a+1)-b2F1(b+1)=0
  2. (c-2a-(b-a)z)2F1+a(1-z)2F1(a+1)-(c-a)2F1(a-1)=0
  3. (c-a-1)2F1+a2F1(a+1)-(c-1)2F1(c-1)=0
  4. (c-a-b)2F1+a(1-z)2F1(a+1)-(c-b)2F1(b-1)=0
  5. (c-a-b)2F1-(c-a)2F1(a-1)+b(1-z)2F1(b+1)=0
  6. (n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)
  7. (n+2)C (n+2)^(lambda)(x)=2(lambda+n+1)xC (n+1)^(lambda)(x)-(2lambda+n)C n^(lambda)(x)
  8. (n+2lambda)C n^(lambda)(x)=2lambda(C n^(lambda+1)(x)-xC (n-1)^(lambda+1)(x))
  9. (z/(1-q))2Phi1(q,q;q^2;z)=Sum z^k/(1-q^k)
  10. *-c functions footer
  11. *-integral functions footer
  12. -log(1-x) less than x/(1-x)
  13. 0!=1
  14. 0F0(;;z)=exp(z)
  15. 0F1(;r;z)0F1(;r;-z)=0F3(r,r/2,r/2+1/2;-z^2/4)
  16. 0F1(;r;z)0F1(;s;z)=2F1(r/2+s/2, r/2+s/2-1/2;r,s,r+s-1;4z)
  17. 1+x greater than exp(x/(1+x)) for nonzero real x greater than -1
  18. 1/B(n,m)=m((n+m-1) choose (n-1))
  19. 1/B(n,m)=n((n+m-1) choose (m-1))
  20. 1/q-number as a q-number
  21. 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)
  22. 1F1(a;r;z)1F1(a;r;-z)=2F3(a,r-a;r,r/2,r/2+1/2;z^2/4)
  23. 1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
  24. 1Phi0(a;;z) as infinite product
  25. 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)
  26. 2F1(1,1;2;z)=-log(1-z)/z
  27. 2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z
  28. 2F1(1/2,1;3/2;-z^2)=arctan(z)/z
  29. 2F1(1/2,1;3/2;z^2)=log((1+z)/(1-z))/(2z)
  30. 2F1(a,b;a+b+1/2;z)^2=3F2(2a,a+b,2b;a+b+1/2,2a+2b;z)
  31. 2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k)
  32. 2cos(mt)cos(nt)=cos((m+n)t)+cos((m-n)t)
  33. Abel p
  34. Abs(e^z-1) less than or equal to e^(abs(z))-1 less than or equal to abs(z)e^(abs(z))
  35. Abs(log(1+z)) less than or equal to -log(1-abs(z))
  36. Abs(log(1-x)) less than 3x/2
  37. Abs(z)/4 less than abs(e^z-1) less than (7abs(z))/4 for 0 less than abs(z) less than 1
  38. Absolute convergence of secant zeta function
  39. Airy Ai
  40. Airy Bi
  41. Airy functions footer
  42. Airy zeta function
  43. Airy zeta function at 2
  44. Alexander operator
  45. Algebraic
  46. Algebraic number
  47. Alternating sum over bottom of binomial coefficient with top fixed equals 0
  48. Anger derivative recurrence
  49. Anger function
  50. Anger of integer order is Bessel J
  51. Anger three-term recurrence
  52. Antiderivative of arccos
  53. Antiderivative of arccosh
  54. Antiderivative of arcsin
  55. Antiderivative of arcsinh
  56. Antiderivative of arctan
  57. Antiderivative of arctanh
  58. Antiderivative of cosine integral
  59. Antiderivative of coth
  60. Antiderivative of hyperbolic cosecant
  61. Antiderivative of inverse error function
  62. Antiderivative of sech
  63. Antiderivative of sine integral
  64. Antiderivative of tanh
  65. Antiderivative of the logarithm
  66. Antiderivative of versine
  67. Apéry's constant
  68. Apéry's constant is irrational
  69. Arakawa-Kaneko zeta function
  70. Arccos
  71. Arccos as inverse cosine
  72. Arccosh
  73. Arccot
  74. Arccoth
  75. Arccsc
  76. Arccsch
  77. Arcsec
  78. Arcsech
  79. Arcsin
  80. Arcsin as inverse sine
  81. Arcsin cdf
  82. Arcsin pdf
  83. Arcsinh
  84. Arctan
  85. Arctanh
  86. Arithmetic functions
  87. Arithmetic zeta function
  88. Artin-Mazur zeta function
  89. Artin constant
  90. Associated Laguerre L
  91. Asymptotic behavior of Sievert integral
  92. Asymptotic formula for partition function
  93. 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
  94. B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt
  95. B(x,y)B(x+y,z)=B(y,z)B(y+z,x)
  96. B(x,y)B(x+y,z)=B(z,x)B(x+z,y)
  97. 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)
  98. B(x,y+1)=(y/(x+y))B(x,y)
  99. B(x,y+1)=(y/x)B(x+1,y)
  100. Barnes G
  101. Barnes G at positive integer
  102. Barnes G at z+1 in terms of Barnes G and gamma
  103. Barnes zeta function
  104. Basic hypergeometric phi
  105. Basic hypergeometric series psi
  106. Bateman F
  107. Bell numbers
  108. Bell polynomial
  109. Bernardi operator
  110. Bernoulli-Euler Gamma function
  111. Bernoulli B
  112. Bernoulli numbers
  113. Bernoulli polynomial and Hurwitz zeta
  114. Bernstein B
  115. Bessel-Clifford
  116. Bessel J
  117. Bessel J in terms of Bessel-Clifford
  118. Bessel Y
  119. Bessel at -n-1/2 in terms of Bessel polynomial
  120. Bessel at n+1/2 in terms of Bessel polynomial
  121. Bessel functions footer
  122. Bessel polynomial
  123. Bessel polynomial generalized hypergeometric
  124. Bessel polynomial in terms of Bessel functions
  125. Beta
  126. Beta as improper integral
  127. Beta as product of gamma functions
  128. Beta in terms of gamma
  129. Beta in terms of power of t over power of (1+t)
  130. Beta in terms of sine and cosine
  131. Beta is symmetric
  132. Bickley-Naylor
  133. Binet's formula
  134. Binomial coefficient
  135. Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1))
  136. Binomial coefficient (n choose 0) equals 1
  137. Binomial coefficient (n choose k) equals (-1)^k ((k-n-1) choose k)
  138. Binomial coefficient (n choose k) equals (n choose (n-k))
  139. Binomial coefficient (n choose n) equals 1
  140. Binomial series
  141. Binomial theorem
  142. Bohr-Mollerup theorem
  143. Bolzano function
  144. Bolzano function is continuous
  145. Bolzano function is nowhere differentiable
  146. Book:Aleksandar Ivić/The Riemann Zeta-Function
  147. Book:Alfred George Greenhill/The applications of elliptic functions
  148. Book:Andrew Gray/A Treatise on Bessel Functions
  149. Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition
  150. Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
  151. Book:Arthur Erdélyi/Higher Transcendental Functions Volume II
  152. Book:Arthur Erdélyi/Higher Transcendental Functions Volume III
  153. Book:Bernard Dwork/Generalized hypergeometric functions
  154. Book:Charalambos Charalambides/Discrete q-Distributions
  155. Book:Earl David Rainville/Special Functions
  156. Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition
  157. Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann
  158. Book:Elena Deza/Figurate Numbers
  159. Book:F.E. Relton/Applied Bessel Functions
  160. Book:G.H. Hardy/The General Theory Of Dirichlet's Series
  161. Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
  162. Book:George E. Andrews/Special Functions
  163. Book:George Eyre Andrews/Number Theory
  164. Book:Harris Hancock/Lectures on the theory of elliptic functions
  165. Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry
  166. Book:Ioannis Dimitrios Avgoustis/Definite Integration using the Generalized Hypergeometric Functions
  167. Book:Johan Thim/Continuous Nowhere Differentiable Functions
  168. Book:Johann Heinrich Graf/Einleitung in die Theorie der Gammafunktion und der Euler'schen Integrale
  169. Book:Larry C. Andrews/Special Functions of Mathematics for Engineers
  170. Book:Leonard Lewin/Dilogarithms and Associated Functions
  171. Book:Leonard Lewin/Polylogarithms and Associated Functions/Second Edition
  172. Book:Leonard Lewin/Structural Properties of Polylogarithms
  173. Book:Michael Wilensky/Ueber Besselsche Funktionen
  174. Book:Milton Abramowitz/Handbook of mathematical functions
  175. Book:Nicholas Higham/Functions of Matrices: Theory and Computation
  176. Book:Norman L. Johnson/Continuous Univariate Distributions Volume 2/Second Edition
  177. Book:Richard Beals/Special functions, a graduate text
  178. Book:Richard Dedekind/Essays on the Theory of Numbers
  179. Book:Roelof Koekoek/Hypergeometric Orthogonal Polynomials and Their q-Analogues
  180. Book:Sir Thomas L. Heath/Euclid: The Thirteen Books of The Elements: Volume 2/Second Edition
  181. Book:T.S. Chihara/An Introduction to Orthogonal Polynomials
  182. Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus
  183. Book:Victor Kac/Quantum Calculus
  184. Book:W.N. Bailey/Generalized Hypergeometric Series
  185. Book:W.W. Bell/Special Functions for Scientists and Engineers
  186. Book:Wilhelm Magnus/Formulas and Theorems for the Special Functions of Mathematical Physics/Third Edition
  187. Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I
  188. Boole polynomials
  189. Brun's constant
  190. Buchstab function
  191. Böhmer C
  192. Böhmer S
  193. C(a-(c-b)z)2F1-ac(1-z)2F1(a+1)+(c-a)(c-b)z2F1(c+1)=0
  194. C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x)
  195. Cahen's constant
  196. Catalan's constant
  197. Catalan's constant using Dirichlet beta
  198. Catalan's constant using Hurwitz zeta
  199. Catalan's constant using Legendre chi
  200. Catalan's identity
  201. Cauchy cdf
  202. Cauchy pdf
  203. Ceiling
  204. Cell
  205. Cellérier function
  206. Cellérier function is continuous
  207. Cellérier function is nowhere differentiable
  208. Chain rule for derivatives
  209. Chaitin's constant
  210. Champernowne constant
  211. Champernowne constant is transcendental
  212. Charlier polynomial
  213. Chebyshev T
  214. Chebyshev U
  215. Chebyshev psi function
  216. Chebyshev theta function
  217. Chi
  218. Clausen cosine
  219. Clausen sine
  220. Closed form for partition function with sinh
  221. Closed formula for physicist's Hermite polynomials
  222. Complex conjugate of argument of error function
  223. Complex number
  224. Constant functions are elliptic functions
  225. Constant multiple rule for derivatives
  226. Continued fraction
  227. Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt
  228. Continued fraction for 2e^(z^2) integral from z to infinity e^(-t^2) dt for positive Re(z)
  229. Continuous
  230. Continuous nowhere differentiable functions footer
  231. Continuous q-Hermite polynomial
  232. Continuous uniform cdf
  233. Continuous uniform pdf
  234. Contour integral representation of reciprocal gamma
  235. Convergence of Hypergeometric pFq
  236. Copeland-Erdős constant
  237. Copeland-Erdős is irrational
  238. Copeland-Erdős is normal
  239. Cosecant
  240. Cosh
  241. Cosh is even
  242. Cosh of a sum
  243. Coshc
  244. Cosine
  245. Cosine integral
  246. Cotangent
  247. Cotangent zeta function
  248. Coth
  249. Coth of a sum
  250. Covercosine

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