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

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=-35/8, b>=a

For fixed z and a=-35/8, b=1/8

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

Input Form

Hypergeometric2F1[-(35/8), 1/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (61636608 - 684021888 z + 3591120555 z^2 - 12350203965 z^3 + 36509137830 z^4 + 88690593342 z^5 - 20029317217 z^6 + 5242870815 z^7 - 949887120 z^8 + 83050240 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (61636608 - 707135616 z + 3841308603 z^2 - 13630092795 z^3 + 40807298070 z^4 - 226602664278 z^5 - 5233101289 z^6 + 1353394497 z^7 - 241364760 z^8 + 20762560 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (61636608 - 684021888 z + 3591120555 z^2 - 12350203965 z^3 + 36509137830 z^4 + 88690593342 z^5 - 20029317217 z^6 + 5242870815 z^7 - 949887120 z^8 + 83050240 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (61636608 - 684021888 z + 3591120555 z^2 - 12350203965 z^3 + 36509137830 z^4 + 88690593342 z^5 - 20029317217 z^6 + 5242870815 z^7 - 949887120 z^8 + 83050240 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (79349907922310025 Pi (1 + Sqrt[1 - z])^(1/4) 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]