Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba6v)

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=11/8

http://functions.wolfram.com/07.23.03.ba6v.01

Input Form

Hypergeometric2F1[-(39/8), 11/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (-23363584 + 196308864 z - 707229691 z^2 + 1366465926 z^3 - 1185412410 z^4 + 1830772552 z^5 - 1451597987 z^6 + 688279098 z^7 - 184271568 z^8 + 21534240 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-23363584 + 196308864 z - 707229691 z^2 + 1366465926 z^3 - 1185412410 z^4 + 1830772552 z^5 - 1451597987 z^6 + 688279098 z^7 - 184271568 z^8 + 21534240 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-23363584 + 196308864 z - 707229691 z^2 + 1366465926 z^3 - 1185412410 z^4 + 1830772552 z^5 - 1451597987 z^6 + 688279098 z^7 - 184271568 z^8 + 21534240 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-23363584 + 210911104 z - 827527051 z^2 + 1789478131 z^3 - 1975687350 z^4 - 4096289498 z^5 + 5109349833 z^6 - 3617632057 z^7 + 1573981032 z^8 - 392230800 z^9 + 43068480 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (1718760866687865 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]