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

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