Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9354)

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=-5/4

http://functions.wolfram.com/07.23.03.9354.01

Input Form

Hypergeometric2F1[-(23/4), -(5/4), 5, z] == (1/(25488471943935 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] (-4 (153824 - 2595780 z + 23924439 z^2 - 200548040 z^3 - 4420162383 z^4 - 4226619306 z^5 - 37754535 z^6 + 5911308 z^7 - 725985 z^8 + 46410 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (615296 - 615296 Sqrt[z] - 9921648 z + 9921648 z^(3/2) + 88328625 z^2 - 88328625 z^(5/2) - 737081345 z^3 + 737081345 z^(7/2) - 5777988762 z^4 + 5777988762 z^(9/2) - 2654364258 z^5 + 2654364258 z^(11/2) + 270055149 z^6 - 270055149 z^(13/2) - 43171245 z^7 + 43171245 z^(15/2) + 5529420 z^8 - 5529420 z^(17/2) - 371280 z^9 + 371280 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]