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

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=-39/8, b>=a

For fixed z and a=-39/8, b=47/8

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

Input Form

Hypergeometric2F1[-(39/8), 47/8, -(11/2), z] == (1/(135168 (1 - z)^(13/2))) (Sqrt[1 - z] (135168 - 111360 z - 110240 z^2 - 149903 z^3 - 270699 z^4 - 766337 z^5 - 6099665 z^6 + 49202780 z^7 - 105907824 z^8 + 104974848 z^9 - 50561280 z^10 + 9630720 z^11) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (33792 - 38400 z - 23348 z^2 - 27781 z^3 - 51909 z^4 - 163163 z^5 - 22311795 z^6 + 91818716 z^7 - 152677008 z^8 + 129051648 z^9 - 55376640 z^10 + 9630720 z^11) 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]