Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm0d)

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=-21/8, b>=a

For fixed z and a=-21/8, b=37/8

http://functions.wolfram.com/07.23.03.bm0d.01

Input Form

Hypergeometric2F1[-(21/8), 37/8, 11/2, z] == (1/(147858095 z^(9/2))) (1024 (-8 Sqrt[z] (-840 - 275 z - 336 z^2 - 756 z^3 - 22719 z^4 + 68238 z^5 - 64872 z^6 + 20400 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((8960 - 4720 z + 779 z^2 + 4746 z^3 + 42651 z^4 - 400032 z^5 + 784992 z^6 - 600576 z^7 + 163200 z^8) Sin[(3 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]