Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6ej)

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=-15/8

http://functions.wolfram.com/07.23.03.b6ej.01

Input Form

Hypergeometric2F1[-(45/8), -(15/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-316440576 + 5605695360 z - 51433262475 z^2 + 354170314050 z^3 - 2631242065725 z^4 - 29956634529412 z^5 - 27058937797085 z^6 - 2524077004350 z^7 + 180854678125 z^8 - 14449943200 z^9 + 681211608 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-316440576 + 5605695360 z - 51433262475 z^2 + 354170314050 z^3 - 2631242065725 z^4 - 29956634529412 z^5 - 27058937797085 z^6 - 2524077004350 z^7 + 180854678125 z^8 - 14449943200 z^9 + 681211608 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-316440576 + 5803470720 z - 54904374555 z^2 + 385756510125 z^3 - 2847584778675 z^4 + 57568876581353 z^5 + 138913308579755 z^6 + 52783661243255 z^7 + 30844362175 z^8 - 2442114125 z^9 + 113535268 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-316440576 + 5605695360 z - 51433262475 z^2 + 354170314050 z^3 - 2631242065725 z^4 - 29956634529412 z^5 - 27058937797085 z^6 - 2524077004350 z^7 + 180854678125 z^8 - 14449943200 z^9 + 681211608 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (22522098222757588455 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]