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

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=-9/8

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

Input Form

Hypergeometric2F1[-(29/8), -(9/8), 19/4, z] == (1/(1752805689 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-4466 + 58667 z - 415657 z^2 + 2854905 z^3 + 36742832 z^4 + 22075529 z^5 - 37789 z^6 + 2139 z^7) + (1/Sqrt[1 - z]) (17864 - 243600 z + 1777729 z^2 - 12222717 z^3 - 31905022 z^4 + 32642230 z^5 + 10527445 z^6 - 628153 z^7 + 34224 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]