Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9pk)

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=-19/4, b>=a

For fixed z and a=-19/4, b=15/4

http://functions.wolfram.com/07.23.03.a9pk.01

Input Form

Hypergeometric2F1[-(19/4), 15/4, 5, z] == (1/(985747455 Pi Sqrt[1 + Sqrt[z]] z^4)) (4096 (4 (1824 + 1824 Sqrt[z] - 988 z - 988 z^(3/2) - 1995 z^2 - 1995 z^(5/2) - 7980 z^3 - 7980 z^(7/2) + 86541 z^4 + 86541 z^(9/2) - 194670 z^5 - 194670 z^(11/2) + 197316 z^6 + 197316 z^(13/2) - 96720 z^7 - 96720 z^(15/2) + 18720 z^8 + 18720 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (7296 - 5776 z - 7505 z^2 - 29925 z^3 - 126651 z^4 + 942249 z^5 - 1873368 z^6 + 1755120 z^7 - 811200 z^8 + 149760 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]