Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7uw)

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=23/4

http://functions.wolfram.com/07.23.03.a7uw.01

Input Form

Hypergeometric2F1[-(23/4), 23/4, 4, z] == (1/(704105325 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((-(736 + 736 Sqrt[z] + 8993 z + 8993 z^(3/2) + 130410 z^2 + 130410 z^(5/2) - 5244375 z^3 - 5244375 z^(7/2) + 29232060 z^4 + 29232060 z^(9/2) - 67918032 z^5 - 67918032 z^(11/2) + 78584064 z^6 + 78584064 z^(13/2) - 44977920 z^7 - 44977920 z^(15/2) + 10183680 z^8 + 10183680 z^(17/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (736 + 8809 z + 128110 z^2 + 223185 z^3 - 15965520 z^4 + 79072968 z^5 - 166153728 z^6 + 177365760 z^7 - 95047680 z^8 + 20367360 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

Standard Form

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MathML Form

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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]