Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.acl9)

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=-13/4, b>=a

For fixed z and a=-13/4, b=9/4

http://functions.wolfram.com/07.23.03.acl9.01

Input Form

Hypergeometric2F1[-(13/4), 9/4, 6, -z] == (1/(8549766225 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-79872 - 438048 z - 881205 z^2 - 609609 z^3 + 315315 z^4 + 2029181 z^5 + 2049894 z^6 + 905520 z^7 + 155232 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-79872 - 378144 z - 606957 z^2 - 195195 z^3 + 405405 z^4 + 677831 z^5 + 381612 z^6 + 77616 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-79872 - 438048 z - 881205 z^2 - 609609 z^3 + 315315 z^4 + 2029181 z^5 + 2049894 z^6 + 905520 z^7 + 155232 z^8) EllipticK[1/2 - 1/(2 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]