Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6fn)

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=-11/8

http://functions.wolfram.com/07.23.03.b6fn.01

Input Form

Hypergeometric2F1[-(45/8), -(11/8), 11/2, z] == (1/(132663219625755 z^(9/2))) (1024 (Sqrt[z] (7210560 - 122021560 z + 1081574343 z^2 - 7552372734 z^3 + 207158917313 z^4 + 510137272584 z^5 + 169909315305 z^6 - 9205940854 z^7 + 1168092927 z^8 - 123454524 z^9 + 6970288 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-9614080 + 170907440 z - 1580746819 z^2 + 11296356225 z^3 - 112029212091 z^4 - 300616007739 z^5 + 237060610939 z^6 + 174373717747 z^7 - 9774991145 z^8 + 1228948903 z^9 - 126939668 z^10 + 6970288 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]