Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b67e)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-35/8

http://functions.wolfram.com/07.23.03.b67e.01

Input Form

Hypergeometric2F1[-(45/8), -(35/8), 11/2, z] == (1/(1817718851363415 z^(9/2))) (1024 (-2 Sqrt[z] (-3605280 + 92299460 z - 1323656019 z^2 + 16418985912 z^3 - 1232009447044 z^4 - 7874361546192 z^5 - 13000083429090 z^6 - 7096667067736 z^7 - 1208371437252 z^8 - 41770657236 z^9 + 183204637 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((9614080 - 254343920 z + 3739665739 z^2 - 46790901150 z^3 + 955822189476 z^4 + 8959267570704 z^5 + 10243005893906 z^6 - 7690730691724 z^7 - 10133368723900 z^8 - 2207342163376 z^9 - 83724519109 z^10 + 366409274 z^11) 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]