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

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=7/4

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

Input Form

Hypergeometric2F1[-(15/4), 7/4, 6, z] == (16384 ((-(22528 + 22528 Sqrt[z] - 155936 z - 155936 z^(3/2) + 437745 z^2 + 437745 z^(5/2) - 582120 z^3 - 582120 z^(7/2) + 150150 z^4 + 150150 z^(9/2) - 263484 z^5 - 263484 z^(11/2) + 184353 z^6 + 184353 z^(13/2) - 64740 z^7 - 64740 z^(15/2) + 9360 z^8 + 9360 z^(17/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (22528 - 161568 z + 475145 z^2 - 681450 z^3 + 270270 z^4 + 397176 z^5 - 605631 z^6 + 398970 z^7 - 134160 z^8 + 18720 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(5492021535 Pi Sqrt[1 + Sqrt[z]] z^5)

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]