Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab7s)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-5/4

http://functions.wolfram.com/07.23.03.ab7s.01

Input Form

Hypergeometric2F1[-(15/4), -(5/4), 4, -z] == (1/(3011753745 Pi z^3)) (256 (1 + z)^(1/4) (2 (-12320 - 174405 z - 1619310 z^2 + 32655354 z^3 - 24504912 z^4 + 109395 z^5 + 6630 z^6) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-12320 - 174405 z - 1619310 z^2 + 32655354 z^3 - 24504912 z^4 + 109395 z^5 + 6630 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (12320 + 165165 z + 1496880 z^2 - 10229874 z^3 + 3301740 z^4 + 208845 z^5 + 13260 z^6) 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]