Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b812)

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.b812.01

Input Form

Hypergeometric2F1[-(43/8), 25/8, 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (120785280 + 102856215 z + 308568645 z^2 - 14155073567 z^3 + 50489710787 z^4 - 79539112800 z^5 + 65861438720 z^6 - 28147159040 z^7 + 4920115200 z^8) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (120785280 + 57561735 z + 257612355 z^2 - 4813087067 z^3 + 15229225409 z^4 - 22414173552 z^5 + 17675208320 z^6 - 7267420160 z^7 + 1230028800 z^8) 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) (120785280 + 102856215 z + 308568645 z^2 - 14155073567 z^3 + 50489710787 z^4 - 79539112800 z^5 + 65861438720 z^6 - 28147159040 z^7 + 4920115200 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (120785280 + 102856215 z + 308568645 z^2 - 14155073567 z^3 + 50489710787 z^4 - 79539112800 z^5 + 65861438720 z^6 - 28147159040 z^7 + 4920115200 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(9702221992155 Pi (1 + Sqrt[1 - z])^(1/4) z^3)

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]