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

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=-23/8, b>=a

For fixed z and a=-23/8, b=-17/8

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

Input Form

Hypergeometric2F1[-(23/8), -(17/8), 11/2, z] == (1/(1175998998603 z^(9/2))) (1024 (Sqrt[z] (10304 - 142232 z + 1009861 z^2 - 5547393 z^3 + 1192803442 z^4 + 1406637222 z^5 + 251991897 z^6 + 2217891 z^7) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-41216 + 597264 z - 4427201 z^2 + 24921650 z^3 - 192413147 z^4 - 259946660 z^5 + 306259737 z^6 + 122831682 z^7 + 2217891 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]