Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9271)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-7/4

http://functions.wolfram.com/07.23.03.9271.01

Input Form

Hypergeometric2F1[-(23/4), -(7/4), -(11/2), z] == (1/(10560 Pi^(3/2))) ((4 Sqrt[z] (2640 - 3840 z + 707 z^2 + 215 z^3 + 104 z^4 + 64 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 4 Sqrt[z] (2640 - 3840 z + 707 z^2 + 215 z^3 + 104 z^4 + 64 z^5) EllipticE[(1/2) (1 + Sqrt[z])] - (-10560 + 5280 Sqrt[z] + 23280 z - 7680 z^(3/2) - 13160 z^2 + 1414 z^(5/2) + 127 z^3 + 430 z^(7/2) + 61 z^4 + 208 z^(9/2) + 32 z^5 + 128 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (10560 + 5280 Sqrt[z] - 23280 z - 7680 z^(3/2) + 13160 z^2 + 1414 z^(5/2) - 127 z^3 + 430 z^(7/2) - 61 z^4 + 208 z^(9/2) - 32 z^5 + 128 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]