Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7ux)

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.a7ux.01

Input Form

Hypergeometric2F1[-(23/4), 23/4, 4, -z] == (1/(704105325 Pi z^3)) (256 (1 + z)^(1/4) (2 (736 - 8993 z + 130410 z^2 + 5244375 z^3 + 29232060 z^4 + 67918032 z^5 + 78584064 z^6 + 44977920 z^7 + 10183680 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (736 - 8993 z + 130410 z^2 + 5244375 z^3 + 29232060 z^4 + 67918032 z^5 + 78584064 z^6 + 44977920 z^7 + 10183680 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-736 + 9545 z - 137655 z^2 + 360840 z^3 + 15604680 z^4 + 63468288 z^5 + 102685440 z^6 + 74680320 z^7 + 20367360 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + 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]