Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4v5)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-17/8

http://functions.wolfram.com/07.23.03.b4v5.01

Input Form

Hypergeometric2F1[-(47/8), -(17/8), 7/2, z] == (1/(800498592663 z^(5/2))) (64 (-4 Sqrt[z] (-100533 + 2580347 z - 3195952929 z^2 - 11840948091 z^3 - 7669051949 z^4 - 335277091 z^5 + 30551529 z^6 - 2966845 z^7 + 165242 z^8) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((1608528 - 42391415 z + 1132336690 z^2 + 8676592239 z^3 + 1243724132 z^4 - 9727621153 z^5 - 1400769310 z^6 + 128057185 z^7 - 12197864 z^8 + 660968 z^9) 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]