Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ae1a)

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=-9/4, b>=a

For fixed z and a=-9/4, b=-9/4

http://functions.wolfram.com/07.23.03.ae1a.01

Input Form

Hypergeometric2F1[-(9/4), -(9/4), 6, z] == (1/(2264274865125 Pi z^5)) (16384 (2 (18432 - 241056 z + 1562187 z^2 - 7150875 z^3 + 32292750 z^4 + 568892522 z^5 + 368802359 z^6 + 29071937 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (18432 - 236448 z + 1505235 z^2 - 6800925 z^3 + 30752550 z^4 + 299481662 z^5 + 161809447 z^6 + 10094175 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (18432 - 241056 z + 1562187 z^2 - 7150875 z^3 + 32292750 z^4 + 568892522 z^5 + 368802359 z^6 + 29071937 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]