Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4sy)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-21/8

http://functions.wolfram.com/07.23.03.b4sy.01

Input Form

Hypergeometric2F1[-(47/8), -(21/8), 3, z] == (256 2^(1/4) (2 Sqrt[1 - z] (-3485144 + 125029541 z + 6005418387 z^2 + 17855281262 z^3 + 9343355182 z^4 + 220575537 z^5 - 16696953 z^6 + 836940 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-3485144 + 125029541 z + 6005418387 z^2 + 17855281262 z^3 + 9343355182 z^4 + 220575537 z^5 - 16696953 z^6 + 836940 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-3485144 + 125029541 z + 6005418387 z^2 + 17855281262 z^3 + 9343355182 z^4 + 220575537 z^5 - 16696953 z^6 + 836940 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 (-871286 + 31801939 z - 1681562072 z^2 - 12591615577 z^3 - 15900190432 z^4 - 3494545327 z^5 + 114828168 z^6 - 8578635 z^7 + 418470 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(1619696713635 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^2)

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]