Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bzd2)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=3/8, b>=a

For fixed z and a=3/8, b=45/8

http://functions.wolfram.com/07.23.03.bzd2.01

Input Form

Hypergeometric2F1[3/8, 45/8, -(9/2), -z] == (1/(7691264 (1 + z)^(21/2))) (2 Sqrt[1 + z] (3845632 + 41340544 z + 204438690 z^2 + 623034231 z^3 + 1360365495 z^4 + 2924017278 z^5 + 922228424 z^6 + 408374315 z^7 + 133261839 z^8 + 26991328 z^9 + 2521168 z^10) Cosh[(3 ArcSinh[Sqrt[z]])/4] - Sqrt[z] (5768448 + 62852048 z + 315175509 z^2 + 973995363 z^3 + 2152631140 z^4 + 6682856310 z^5 + 2222692653 z^6 + 943577783 z^7 + 292884714 z^8 + 56503824 z^9 + 5042336 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]