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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(11/2), z] == (1/676831232) ((1/(1 - Sqrt[z])^(25/4)) (338415616 - 2115097600 Sqrt[z] + 7239402240 z - 18410963200 z^(3/2) + 38885348320 z^2 - 72171847020 z^(5/2) + 121470612055 z^3 - 189021504100 z^(7/2) + 274974963120 z^4 - 376109676800 z^(9/2) + 483109442816 z^5 - 577421644800 z^(11/2) + 615916421120 z^6 - 530038784000 z^(13/2) + 321148354560 z^7 - 116424704000 z^(15/2) + 18627952640 z^8) + (1/(1 + Sqrt[z])^(25/4)) (338415616 + 2115097600 Sqrt[z] + 7239402240 z + 18410963200 z^(3/2) + 38885348320 z^2 + 72171847020 z^(5/2) + 121470612055 z^3 + 189021504100 z^(7/2) + 274974963120 z^4 + 376109676800 z^(9/2) + 483109442816 z^5 + 577421644800 z^(11/2) + 615916421120 z^6 + 530038784000 z^(13/2) + 321148354560 z^7 + 116424704000 z^(15/2) + 18627952640 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]