Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ac9z)

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=-7/4

http://functions.wolfram.com/07.23.03.ac9z.01

Input Form

Hypergeometric2F1[-(13/4), -(7/4), 6, -z] == (1/(4803747223275 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-26624 - 365664 z - 2508519 z^2 - 12295569 z^3 - 60566220 z^4 + 769053582 z^5 - 490885263 z^6 + 32403987 z^7 + 605682 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-26624 - 345696 z - 2252367 z^2 - 10645635 z^3 - 52831350 z^4 + 221126202 z^5 - 69996267 z^6 + 302841 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-26624 - 365664 z - 2508519 z^2 - 12295569 z^3 - 60566220 z^4 + 769053582 z^5 - 490885263 z^6 + 32403987 z^7 + 605682 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]