Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b81a)

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=-43/8, b>=a

For fixed z and a=-43/8, b=25/8

http://functions.wolfram.com/07.23.03.b81a.01

Input Form

Hypergeometric2F1[-(43/8), 25/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (883458048 - 4006620288 z + 4651176915 z^2 + 2185458660 z^3 + 3130980930 z^4 - 65433801948 z^5 + 152908962883 z^6 - 171090887520 z^7 + 106004532480 z^8 - 35199324160 z^9 + 4920115200 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (883458048 - 4337917056 z + 6063070563 z^2 + 803977020 z^3 + 2021266170 z^4 - 20886680868 z^5 + 44330408251 z^6 - 47026803888 z^7 + 28041552000 z^8 - 9030461440 z^9 + 1230028800 z^10) 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) (883458048 - 4006620288 z + 4651176915 z^2 + 2185458660 z^3 + 3130980930 z^4 - 65433801948 z^5 + 152908962883 z^6 - 171090887520 z^7 + 106004532480 z^8 - 35199324160 z^9 + 4920115200 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (883458048 - 4006620288 z + 4651176915 z^2 + 2185458660 z^3 + 3130980930 z^4 - 65433801948 z^5 + 152908962883 z^6 - 171090887520 z^7 + 106004532480 z^8 - 35199324160 z^9 + 4920115200 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(12079266380232975 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]