Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a87g)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-17/4

http://functions.wolfram.com/07.23.03.a87g.01

Input Form

Hypergeometric2F1[-(21/4), -(17/4), 5, z] == (1/(32763925569375 Pi z^4)) (4096 (2 (-84864 + 2153424 z - 32146881 z^2 + 485592471 z^3 + 38752916075 z^4 + 144717766931 z^5 + 143254065309 z^6 + 42073294789 z^7 + 2872176121 z^8 + 5287425 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 2 Sqrt[1 - z] (-42432 + 1066104 z - 15811887 z^2 + 238965090 z^3 + 11435416975 z^4 + 38049262388 z^5 + 33942823199 z^6 + 8868195538 z^7 + 512880225 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-84864 + 2153424 z - 32146881 z^2 + 485592471 z^3 + 38752916075 z^4 + 144717766931 z^5 + 143254065309 z^6 + 42073294789 z^7 + 2872176121 z^8 + 5287425 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </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> <plus /> <apply> <times /> <cn type='integer'> 512880225 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8868195538 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33942823199 </cn> <apply> <power /> 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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]