Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9x3)

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=25/8, b>=a

For fixed z and a=25/8, b=45/8

http://functions.wolfram.com/07.23.03.c9x3.01

Input Form

Hypergeometric2F1[25/8, 45/8, -(7/4), z] == (1/(30044 2^(3/4) (-1 + z)^10)) ((1 + Sqrt[1 - z])^(3/4) (2 (7511 - 149147 z - 94222680 z^2 - 229515742 z^3 - 86759009 z^4 - 284487 z^5 + 12834 z^6) + (1/Sqrt[1 - z]) (15022 - 305805 z + 198350223 z^2 + 576071774 z^3 + 304183596 z^4 + 18200751 z^5 - 787865 z^6 + 34224 z^7)))

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]