Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b80u)

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=-43/8, b>=a

For fixed z and a=-43/8, b=25/8

http://functions.wolfram.com/07.23.03.b80u.01

Input Form

Hypergeometric2F1[-(43/8), 25/8, 9/4, z] == (2 2^(1/4) (-188727 + 18888942 z - 112362407 z^2 + 259658864 z^3 - 292251520 z^4 + 161368064 z^5 - 35143680 z^6 + (1/Sqrt[1 - z]) (188727 + 37572915 z - 332237483 z^2 + 1089719841 z^3 - 1794938080 z^4 + 1601236736 z^5 - 742117376 z^6 + 140574720 z^7)))/ (113112441 (1 + Sqrt[1 - z])^(1/4) z)

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]