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

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=39/8

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

Input Form

Hypergeometric2F1[-(39/8), 39/8, 7/2, z] == (1/(51625413 z^(5/2))) (64 (-2 Sqrt[z] (-78 - 923 z - 423068 z^2 + 3055333 z^3 - 8166352 z^4 + 10394064 z^5 - 6391296 z^6 + 1532160 z^7) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((624 + 6955 z + 152828 z^2 - 2743609 z^3 + 12357714 z^4 - 25320464 z^5 + 26796384 z^6 - 14314752 z^7 + 3064320 z^8) Sin[ArcSin[Sqrt[z]]/4])))

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]