Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ri)

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=17/4

http://functions.wolfram.com/07.23.03.a9ri.01

Input Form

Hypergeometric2F1[-(19/4), 17/4, 6, z] == (1/(214188839865 Pi z^5)) (16384 (2 Sqrt[1 - z] (428032 - 541728 z - 541101 z^2 - 803187 z^3 - 2277891 z^4 + 37901859 z^5 - 88619136 z^6 + 90114048 z^7 - 43843584 z^8 + 8388608 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (428032 - 862752 z - 164901 z^2 - 373065 z^3 - 1628319 z^4 + 13542909 z^5 - 27241104 z^6 + 25340928 z^7 - 11550720 z^8 + 2097152 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (428032 - 541728 z - 541101 z^2 - 803187 z^3 - 2277891 z^4 + 37901859 z^5 - 88619136 z^6 + 90114048 z^7 - 43843584 z^8 + 8388608 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]