Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5e1)

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.b5e1.01

Input Form

Hypergeometric2F1[-(47/8), 23/8, 7/2, z] == (1/(38047929381 z^(5/2))) (64 (Sqrt[z] (1742572 + 3920787 z + 632188823 z^2 - 3254908415 z^3 + 7178981953 z^4 - 8633300104 z^5 + 5933991536 z^6 - 2201221440 z^7 + 343335168 z^8) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-6970288 - 10891075 z - 139405760 z^2 + 1723203594 z^3 - 6059514208 z^4 + 10878047873 z^5 - 11346601640 z^6 + 6991685360 z^7 - 2372889024 z^8 + 343335168 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]