Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9864)

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/07.23.03.9864.01

Input Form

Hypergeometric2F1[-(23/4), 13/4, 6, z] == (1/(4959295446105 Pi z^5)) (16384 (-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[(1/2) (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[(1/2) (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[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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<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]