Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7t6)

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=21/4

http://functions.wolfram.com/07.23.03.a7t6.01

Input Form

Hypergeometric2F1[-(23/4), 21/4, 5, z] == (1/(6068683796175 Pi z^4)) (4096 (-2 Sqrt[1 - z] (615296 + 2845744 z + 13973949 z^2 + 111512786 z^3 - 4842303695 z^4 + 21899407392 z^5 - 42063357952 z^6 + 41159753728 z^7 - 20308819968 z^8 + 4026531840 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + 2 (307648 + 1192136 z + 5898189 z^2 + 50406202 z^3 - 981899995 z^4 + 3723555516 z^5 - 6416845568 z^6 + 5794070528 z^7 - 2680160256 z^8 + 503316480 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (615296 + 2845744 z + 13973949 z^2 + 111512786 z^3 - 4842303695 z^4 + 21899407392 z^5 - 42063357952 z^6 + 41159753728 z^7 - 20308819968 z^8 + 4026531840 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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<cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2845744 </cn> <ci> z </ci> </apply> <cn type='integer'> 615296 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </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]