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

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=-7/4, b>=a

For fixed z and a=-7/4, b=3/4

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

Input Form

Hypergeometric2F1[-(7/4), 3/4, 6, z] == (1/(3011753745 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((14336 - 100128 z + 302421 z^2 - 519897 z^3 + 587853 z^4 + 49725 z^5 - 6630 z^6) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-14336 + 14336 Sqrt[z] + 89376 z - 89376 z^(3/2) - 237069 z^2 + 237069 z^(5/2) + 351939 z^3 - 351939 z^(7/2) - 348075 z^4 + 348075 z^(9/2) + 89505 z^5 - 89505 z^(11/2) - 13260 z^6 + 13260 z^(13/2)) 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]