Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ad01)

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=-11/4, b>=a

For fixed z and a=-11/4, b=-9/4

http://functions.wolfram.com/07.23.03.ad01.01

Input Form

Hypergeometric2F1[-(11/4), -(9/4), 6, -z] == (1/(4512611027925 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-22528 - 312224 z - 2168001 z^2 - 10808325 z^3 - 54606090 z^4 + 729762774 z^5 - 516305733 z^6 + 50432703 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-22528 - 295328 z - 1949145 z^2 - 9380085 z^3 - 47786970 z^4 + 213727254 z^5 - 79330461 z^6 + 2403375 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-22528 - 312224 z - 2168001 z^2 - 10808325 z^3 - 54606090 z^4 + 729762774 z^5 - 516305733 z^6 + 50432703 z^7) 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]