Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.buo0)

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=-5/8, b>=a

For fixed z and a=-5/8, b=15/8

http://functions.wolfram.com/07.23.03.buo0.01

Input Form

Hypergeometric2F1[-(5/8), 15/8, -(21/4), z] == (1/(297024 2^(1/4) (-1 + z)^6)) ((1 + Sqrt[1 - z])^(1/4) (2 (74256 - 424320 z + 987363 z^2 - 1169277 z^3 + 686203 z^4 - 97643 z^5 + 27898 z^6) + (1/Sqrt[1 - z]) (148512 - 922896 z + 2380482 z^2 - 3229119 z^3 + 2342081 z^4 - 683501 z^5 - 934583 z^6 + 223184 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]