Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bk9t)

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=23/8

http://functions.wolfram.com/07.23.03.bk9t.01

Input Form

Hypergeometric2F1[-(23/8), 23/8, -(11/2), z] == -((1/(135168 (1 - z)^(11/2))) (Sqrt[1 - z] (-135168 + 476928 z - 513376 z^2 + 85163 z^3 + 54340 z^4 + 62647 z^5 + 149578 z^6 - 249392 z^7 + 86944 z^8) Cos[ArcSin[Sqrt[z]]/4] + 2 Sqrt[z] (-16896 + 64896 z - 80558 z^2 + 24089 z^3 + 8255 z^4 + 6799 z^5 + 131703 z^6 - 146432 z^7 + 43472 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]