Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9pu)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-29/8

http://functions.wolfram.com/07.23.03.b9pu.01

Input Form

Hypergeometric2F1[-(39/8), -(29/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-825756672 + 18175248416 z - 233106646409 z^2 + 3006375216390 z^3 + 71312944041865 z^4 + 150632083784180 z^5 + 75644291121945 z^6 + 8079341462790 z^7 + 19617245895 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-825756672 + 18175248416 z - 233106646409 z^2 + 3006375216390 z^3 + 71312944041865 z^4 + 150632083784180 z^5 + 75644291121945 z^6 + 8079341462790 z^7 + 19617245895 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-825756672 + 18175248416 z - 233106646409 z^2 + 3006375216390 z^3 + 71312944041865 z^4 + 150632083784180 z^5 + 75644291121945 z^6 + 8079341462790 z^7 + 19617245895 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-412878336 + 9345673168 z - 122190752177 z^2 + 1575121443805 z^3 - 50367481255465 z^4 - 243890300465875 z^5 - 252463862009515 z^6 - 68323844898465 z^7 - 3393783539835 z^8 + 19617245895 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5576850641068782075 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]