Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm82)

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=-21/8, b>=a

For fixed z and a=-21/8, b=47/8

http://functions.wolfram.com/07.23.03.bm82.01

Input Form

Hypergeometric2F1[-(21/8), 47/8, 23/4, z] == (1/(276758793 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (6160 + 13244 z + 32585 z^2 + 104939 z^3 + 638448 z^4 - 4659072 z^5 + 6555648 z^6 - 2703360 z^7 - (1/Sqrt[1 - z]) (6160 + 10164 z + 25193 z^2 + 86606 z^3 + 580837 z^4 - 13642848 z^5 + 35777280 z^6 - 33656832 z^7 + 10813440 z^8)))

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]