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

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=1/8, b>=a

For fixed z and a=1/8, b=13/8

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

Input Form

Hypergeometric2F1[1/8, 13/8, -(23/4), z] == (1/(1538240 2^(3/4) (-1 + z)^7)) ((1 + Sqrt[1 - z])^(3/4) (-769120 + 5266800 z - 15403190 z^2 + 24923569 z^3 - 24105711 z^4 + 14052275 z^5 + 1306929 z^6 + (1/Sqrt[1 - z]) (2 (-384560 + 2825680 z - 8970225 z^2 + 16007442 z^3 - 17470614 z^4 + 11883840 z^5 - 8277217 z^6 + 871286 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]