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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-15/4, b>=a

For fixed z and a=-15/4, b=21/4

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

Input Form

Hypergeometric2F1[-(15/4), 21/4, 3/2, z] == (1/(2197845 Pi^(3/2) Sqrt[z])) (2 (2 (266805 - 10189440 z + 58767360 z^2 - 105971712 z^3 + 58720256 z^4) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (266805 - 10189440 z + 58767360 z^2 - 105971712 z^3 + 58720256 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (266805 - 965520 Sqrt[z] - 10189440 z + 9477120 z^(3/2) + 58767360 z^2 - 22364160 z^(5/2) - 105971712 z^3 + 14680064 z^(7/2) + 58720256 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (266805 + 965520 Sqrt[z] - 10189440 z - 9477120 z^(3/2) + 58767360 z^2 + 22364160 z^(5/2) - 105971712 z^3 - 14680064 z^(7/2) + 58720256 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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]