Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9394)

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=-3/4

http://functions.wolfram.com/07.23.03.9394.01

Input Form

Hypergeometric2F1[-(23/4), -(3/4), 6, z] == (1/(551032827345 Pi z^5)) (16384 (2 Sqrt[1 - z] (2048 - 30496 z + 227363 z^2 - 1211402 z^3 + 6460909 z^4 + 36626996 z^5 + 6460909 z^6 - 1211402 z^7 + 227363 z^8 - 30496 z^9 + 2048 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (2048 - 32032 z + 250091 z^2 - 1379846 z^3 + 7354417 z^4 - 35405020 z^5 - 65571107 z^6 - 317894 z^7 + 58919 z^8 - 7768 z^9 + 512 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (2048 - 30496 z + 227363 z^2 - 1211402 z^3 + 6460909 z^4 + 36626996 z^5 + 6460909 z^6 - 1211402 z^7 + 227363 z^8 - 30496 z^9 + 2048 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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</apply> <cn type='integer'> 2048 </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> </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]