Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5dy)

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=23/8

http://functions.wolfram.com/07.23.03.b5dy.01

Input Form

Hypergeometric2F1[-(47/8), 23/8, 5/2, z] == (1/(2839397715 z^(3/2))) (16 (Sqrt[z] (435643 + 186365811 z - 1336888047 z^2 + 3790295113 z^3 - 5574339320 z^4 + 4531424304 z^5 - 1940951232 z^6 + 343335168 z^7) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1742572 - 34415797 z + 598442223 z^2 - 2752026871 z^3 + 6118934657 z^4 - 7618891016 z^5 + 5458983024 z^6 - 2112618816 z^7 + 343335168 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]