Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4sc)

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=-25/8

http://functions.wolfram.com/07.23.03.b4sc.01

Input Form

Hypergeometric2F1[-(47/8), -(25/8), 7/2, z] == (1/(2401495777989 z^(5/2))) (64 (Sqrt[z] (670220 - 20944375 z + 38238100946 z^2 + 206829570247 z^3 + 247812856908 z^4 + 70215102663 z^5 + 1522426050 z^6 - 63494775 z^7 + 2253300 z^8) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-2680880 + 85620605 z - 2916294775 z^2 - 33348378051 z^3 - 34218139427 z^4 + 40031847891 z^5 + 28876500987 z^6 + 1553891775 z^7 - 64621425 z^8 + 2253300 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]