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

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=45/8

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

Input Form

Hypergeometric2F1[41/8, 45/8, -(7/4), z] == (1/(150220 2^(3/4) (-1 + z)^12)) ((1 + Sqrt[1 - z])^(3/4) (-2 (-37555 + 1062270 z + 1487931495 z^2 + 7210331508 z^3 + 8055097035 z^4 + 2358865198 z^5 + 132313953 z^6) + (1/Sqrt[1 - z]) (75110 - 2162095 z + 3082680140 z^2 + 16749231571 z^3 + 22122353782 z^4 + 8530375319 z^5 + 829734392 z^6 + 9215525 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]