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

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=-35/8, b>=a

For fixed z and a=-35/8, b=1/8

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

Input Form

Hypergeometric2F1[-(35/8), 1/8, 17/4, z] == (8 2^(1/4) (-22572 + 237633 z - 1331748 z^2 + 29708566 z^3 - 655520 z^4 + 224145 z^5 - 51000 z^6 + 5440 z^7 + (1/Sqrt[1 - z]) (22572 - 248919 z + 1447743 z^2 + 6512074 z^3 - 10118230 z^4 + 3222605 z^5 - 1035045 z^6 + 218960 z^7 - 21760 z^8)))/ (294865765 (1 + Sqrt[1 - z])^(1/4) z^3)

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]