Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9865)

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=13/4

http://functions.wolfram.com/07.23.03.9865.01

Input Form

Hypergeometric2F1[-(23/4), 13/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (9844736 + 40763360 z + 34624821 z^2 - 35937132 z^3 + 72076158 z^4 + 844598580 z^5 + 1877398005 z^6 + 2065872768 z^7 + 1270953984 z^8 + 420675584 z^9 + 58720256 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (9844736 + 50608096 z + 75388181 z^2 - 1312311 z^3 + 36139026 z^4 + 916674738 z^5 + 2721996585 z^6 + 3943270773 z^7 + 3336826752 z^8 + 1691629568 z^9 + 479395840 z^10 + 58720256 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (9844736 + 48146912 z + 64505133 z^2 - 12517428 z^3 + 43810998 z^4 + 296254476 z^5 + 581043141 z^6 + 593416944 z^7 + 345424896 z^8 + 109297664 z^9 + 14680064 z^10) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (9844736 + 40763360 z + 34624821 z^2 - 35937132 z^3 + 72076158 z^4 + 844598580 z^5 + 1877398005 z^6 + 2065872768 z^7 + 1270953984 z^8 + 420675584 z^9 + 58720256 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4959295446105 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 34624821 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40763360 </cn> <ci> z </ci> </apply> <cn type='integer'> 9844736 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4959295446105 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <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]