Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab5g)

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=-7/4

http://functions.wolfram.com/07.23.03.ab5g.01

Input Form

Hypergeometric2F1[-(15/4), -(7/4), -(11/2), z] == (1/(10560 Pi^(3/2))) ((4 Sqrt[z] (2640 - 2160 z + 147 z^2 + 14 z^3) EllipticE[(1/2) (1 - Sqrt[z])] - 4 Sqrt[z] (2640 - 2160 z + 147 z^2 + 14 z^3) EllipticE[(1/2) (1 + Sqrt[z])] - (-10560 + 5280 Sqrt[z] + 16560 z - 4320 z^(3/2) - 5880 z^2 + 294 z^(5/2) + 7 z^3 + 28 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (10560 + 5280 Sqrt[z] - 16560 z - 4320 z^(3/2) + 5880 z^2 + 294 z^(5/2) - 7 z^3 + 28 z^(7/2)) 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]