Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ad2g)

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=-5/4

http://functions.wolfram.com/07.23.03.ad2g.01

Input Form

Hypergeometric2F1[-(11/4), -(5/4), 4, z] == (1/(334639305 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((2464 - 29645 z + 226996 z^2 + 3462258 z^3 + 1839636 z^4 + 3315 z^5) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-2464 + 2464 Sqrt[z] + 27797 z - 27797 z^(3/2) - 206437 z^2 + 206437 z^(5/2) - 999567 z^3 + 999567 z^(7/2) - 202215 z^4 + 202215 z^(9/2) + 6630 z^5 - 6630 z^(11/2)) 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]