Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ac)

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=-3/4

http://functions.wolfram.com/07.23.03.a9ac.01

Input Form

Hypergeometric2F1[-(19/4), -(3/4), 4, z] == (1/(140821065 Pi z^3)) (256 (-2 Sqrt[1 - z] (-608 + 8493 z - 77292 z^2 - 660170 z^3 - 142284 z^4 + 27333 z^5 - 4496 z^6 + 384 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-608 + 8949 z - 83619 z^2 + 497386 z^3 + 1269090 z^4 + 7137 z^5 - 1151 z^6 + 96 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-608 + 8493 z - 77292 z^2 - 660170 z^3 - 142284 z^4 + 27333 z^5 - 4496 z^6 + 384 z^7) EllipticK[(1/2) (1 - Sqrt[1 - 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]