Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7w7)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-11/2, b>=a

For fixed z and a=-11/2, b=-21/4

http://functions.wolfram.com/07.23.03.a7w7.01

Input Form

Hypergeometric2F1[-(11/2), -(21/4), 4, z] == (2 (14336 - 500864 z + 13603968 z^2 + 1463836480 z^3 + 8478744800 z^4 + 13502410392 z^5 + 7025414672 z^6 + 1104146386 z^7 + 34482315 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (14336 - 500864 z + 13603968 z^2 + 1463836480 z^3 + 8478744800 z^4 + 13502410392 z^5 + 7025414672 z^6 + 1104146386 z^7 + 34482315 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (14336 - 493696 z + 13359360 z^2 + 730200640 z^3 + 3409760800 z^4 + 4397222232 z^5 + 1786805528 z^6 + 200483570 z^7 + 3364725 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (14336 - 500864 z + 13603968 z^2 + 1463836480 z^3 + 8478744800 z^4 + 13502410392 z^5 + 7025414672 z^6 + 1104146386 z^7 + 34482315 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (14336 - 500864 z + 13603968 z^2 + 1463836480 z^3 + 8478744800 z^4 + 13502410392 z^5 + 7025414672 z^6 + 1104146386 z^7 + 34482315 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (14336 - 500864 z + 13603968 z^2 + 1463836480 z^3 + 8478744800 z^4 + 13502410392 z^5 + 7025414672 z^6 + 1104146386 z^7 + 34482315 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (185059875 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)

Standard Form

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MathML 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]