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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-1/8

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

Input Form

Hypergeometric2F1[-(29/8), -(1/8), 19/4, z] == (1/(5258417067 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-232232 + 2427880 z - 12783693 z^2 + 57347732 z^3 + 377731626 z^4 - 3311172 z^5 + 601059 z^6 - 57040 z^7 - (1/Sqrt[1 - z]) (4 (-58058 + 635999 z - 3492151 z^2 + 15862652 z^3 + 5465496 z^4 - 21550425 z^5 + 3719721 z^6 - 640274 z^7 + 57040 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]