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

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=-17/4, b>=a

For fixed z and a=-17/4, b=23/4

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

Input Form

Hypergeometric2F1[-(17/4), 23/4, 6, -z] == (16384 Sqrt[2] ((1357824 - 2439840 z + 5846997 z^2 - 19260150 z^3 + 111690969 z^4 + 3431592756 z^5 + 11249090560 z^6 + 14948261888 z^7 + 9101639680 z^8 + 2113929216 z^9) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (1357824 - 2439840 z + 5846997 z^2 - 19260150 z^3 + 111690969 z^4 + 3431592756 z^5 + 11249090560 z^6 + 14948261888 z^7 + 9101639680 z^8 + 2113929216 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (1357824 - 2779296 z + 6700941 z^2 - 21360534 z^3 + 118090245 z^4 + 1197773376 z^5 + 2413336576 z^6 + 1895563264 z^7 + 528482304 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (1357824 - 2439840 z + 5846997 z^2 - 19260150 z^3 + 111690969 z^4 + 3431592756 z^5 + 11249090560 z^6 + 14948261888 z^7 + 9101639680 z^8 + 2113929216 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (18031456968525 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

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]