Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8o0)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-37/8

http://functions.wolfram.com/07.23.03.b8o0.01

Input Form

Hypergeometric2F1[-(41/8), -(37/8), 7/4, z] == (2^(3/4) (8 (36167977 + 509543771 z + 1487512314 z^2 + 1227918166 z^3 + 282428717 z^4 + 12674559 z^5) + (1/Sqrt[1 - z]) (285604411 + 3460513230 z + 5944253061 z^2 - 3140329660 z^3 - 5503111275 z^4 - 1028520306 z^5 - 18409461 z^6)))/ (574948227 (1 + Sqrt[1 - z])^(3/4))

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]