Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9m0)

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=11/4

http://functions.wolfram.com/07.23.03.a9m0.01

Input Form

Hypergeometric2F1[-(19/4), 11/4, 6, z] == (1/(115332452235 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 2267232 z + 3883011 z^2 - 790020 z^3 - 1711710 z^4 + 8055684 z^5 - 11141949 z^6 + 7747272 z^7 - 2779920 z^8 + 411840 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 1946208 z - 1946208 z^(3/2) - 2473515 z^2 + 2473515 z^(5/2) - 855855 z^3 + 855855 z^(7/2) + 855855 z^4 - 855855 z^(9/2) + 6493851 z^5 - 6493851 z^(11/2) - 13728624 z^6 + 13728624 z^(13/2) + 11849760 z^7 - 11849760 z^(15/2) - 4942080 z^8 + 4942080 z^(17/2) + 823680 z^9 - 823680 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]