Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ya)

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=-9/2, b>=a

For fixed z and a=-9/2, b=-17/4

http://functions.wolfram.com/07.23.03.a9ya.01

Input Form

Hypergeometric2F1[-(9/2), -(17/4), 5, z] == (8 Sqrt[2] (2 (-4096 + 95232 z - 1289792 z^2 + 17467520 z^3 + 928189600 z^4 + 2788677888 z^5 + 2131990124 z^6 + 442142976 z^7 + 17161045 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-4096 + 95232 z - 1289792 z^2 + 17467520 z^3 + 928189600 z^4 + 2788677888 z^5 + 2131990124 z^6 + 442142976 z^7 + 17161045 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-4096 + 93184 z - 1243840 z^2 + 16859840 z^3 + 427517600 z^4 + 994765248 z^5 + 583052228 z^6 + 85340860 z^7 + 1762475 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-4096 + 95232 z - 1289792 z^2 + 17467520 z^3 + 928189600 z^4 + 2788677888 z^5 + 2131990124 z^6 + 442142976 z^7 + 17161045 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-4096 + 95232 z - 1289792 z^2 + 17467520 z^3 + 928189600 z^4 + 2788677888 z^5 + 2131990124 z^6 + 442142976 z^7 + 17161045 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-4096 + 95232 z - 1289792 z^2 + 17467520 z^3 + 928189600 z^4 + 2788677888 z^5 + 2131990124 z^6 + 442142976 z^7 + 17161045 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (2035658625 Pi Sqrt[1 + Sqrt[1 - z]] z^4)

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]