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

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=11/4

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

Input Form

Hypergeometric2F1[-(11/4), 11/4, 6, z] == (16384 ((22528 + 22528 Sqrt[z] - 93984 z - 93984 z^(3/2) + 122001 z^2 + 122001 z^(5/2) - 15675 z^3 - 15675 z^(7/2) - 27225 z^4 - 27225 z^(9/2) + 69615 z^5 + 69615 z^(11/2) - 47100 z^6 - 47100 z^(13/2) + 10800 z^7 + 10800 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (22528 - 99616 z + 143913 z^2 - 40425 z^3 - 28875 z^4 - 79875 z^5 + 160350 z^6 - 99600 z^7 + 21600 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(1267389585 Pi Sqrt[1 + Sqrt[z]] z^5)

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]