Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9446)

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=-1/4

http://functions.wolfram.com/07.23.03.9446.01

Input Form

Hypergeometric2F1[-(23/4), -(1/4), 5, z] == (1/(6068683796175 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-615296 + 8383408 z - 58890557 z^2 + 340696125 z^3 + 3642885090 z^4 + 126398298 z^5 - 41625129 z^6 + 11063481 z^7 - 1922700 z^8 + 159120 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 2 (307648 - 307648 Sqrt[z] - 3960968 z + 3960968 z^(3/2) + 26510605 z^2 - 26510605 z^(5/2) - 150915765 z^3 + 150915765 z^(7/2) - 450077550 z^4 + 450077550 z^(9/2) + 101201646 z^5 - 101201646 z^(11/2) - 34460751 z^6 + 34460751 z^(13/2) + 9722895 z^7 - 9722895 z^(15/2) - 1803360 z^8 + 1803360 z^(17/2) + 159120 z^9 - 159120 z^(19/2)) 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]