Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6bp)

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=-23/8

http://functions.wolfram.com/07.23.03.b6bp.01

Input Form

Hypergeometric2F1[-(45/8), -(23/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (35160064 - 716248960 z + 7723749075 z^2 - 64360820125 z^3 + 602262962875 z^4 + 10150208239703 z^5 + 15871604884765 z^6 + 5413506430425 z^7 + 215910535225 z^8 - 7289480275 z^9 + 216749148 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (35160064 - 716248960 z + 7723749075 z^2 - 64360820125 z^3 + 602262962875 z^4 + 10150208239703 z^5 + 15871604884765 z^6 + 5413506430425 z^7 + 215910535225 z^8 - 7289480275 z^9 + 216749148 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (35160064 - 738224000 z + 8167799395 z^2 - 69116409775 z^3 + 641729887925 z^4 - 16367996992907 z^5 - 59782597198345 z^6 - 45509015284045 z^7 - 7675687846025 z^8 - 1225664825 z^9 + 36124858 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (35160064 - 716248960 z + 7723749075 z^2 - 64360820125 z^3 + 602262962875 z^4 + 10150208239703 z^5 + 15871604884765 z^6 + 5413506430425 z^7 + 215910535225 z^8 - 7289480275 z^9 + 216749148 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (6854551633013179095 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

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]