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

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=-15/4, b>=a

For fixed z and a=-15/4, b=23/4

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

Input Form

Hypergeometric2F1[-(15/4), 23/4, 5, z] == (4096 ((-(384 + 384 Sqrt[z] + 1808 z + 1808 z^(3/2) + 8421 z^2 + 8421 z^(5/2) + 59619 z^3 + 59619 z^(7/2) - 1032456 z^4 - 1032456 z^(9/2) + 2697552 z^5 + 2697552 z^(11/2) - 2583360 z^6 - 2583360 z^(13/2) + 848640 z^7 + 848640 z^(15/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 2 (192 + 856 z + 3971 z^2 + 28686 z^3 + 129207 z^4 - 1463952 z^5 + 3247920 z^6 - 2795520 z^7 + 848640 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(2675600235 Pi Sqrt[1 + Sqrt[z]] z^4)

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]