Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8aq)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-11/4

http://functions.wolfram.com/07.23.03.a8aq.01

Input Form

Hypergeometric2F1[-(21/4), -(11/4), 5, -z] == (1/(26930098069875 Pi z^4)) (4096 (1 + z)^(1/4) (-2 (198016 + 4084080 z + 48122529 z^2 + 552288282 z^3 - 20360405433 z^4 + 43648506432 z^5 - 20049982785 z^6 + 1370254578 z^7 + 39066489 z^8 + 1211364 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 2 Sqrt[1 + z] (99008 + 1967784 z + 22597029 z^2 + 259422618 z^3 - 3797474865 z^4 + 5306353956 z^5 - 1385708877 z^6 + 9489018 z^7 + 302841 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (198016 + 4084080 z + 48122529 z^2 + 552288282 z^3 - 20360405433 z^4 + 43648506432 z^5 - 20049982785 z^6 + 1370254578 z^7 + 39066489 z^8 + 1211364 z^9) 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]