Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8ap)

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.a8ap.01

Input Form

Hypergeometric2F1[-(21/4), -(11/4), 5, z] == (1/(26930098069875 Pi z^4)) (4096 Sqrt[1 + Sqrt[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) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-99008 + 99008 Sqrt[z] + 1967784 z - 1967784 z^(3/2) - 22597029 z^2 + 22597029 z^(5/2) + 259422618 z^3 - 259422618 z^(7/2) + 3797474865 z^4 - 3797474865 z^(9/2) + 5306353956 z^5 - 5306353956 z^(11/2) + 1385708877 z^6 - 1385708877 z^(13/2) + 9489018 z^7 - 9489018 z^(15/2) - 302841 z^8 + 302841 z^(17/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]