Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ag28)

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=-5/4, b>=a

For fixed z and a=-5/4, b=9/4

http://functions.wolfram.com/07.23.03.ag28.01

Input Form

Hypergeometric2F1[-(5/4), 9/4, 6, z] == (1/(26801775 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((-(-2048 - 2048 Sqrt[z] + 8416 z + 8416 z^(3/2) - 12035 z^2 - 12035 z^(5/2) + 5390 z^3 + 5390 z^(7/2) + 1925 z^4 + 1925 z^(9/2) - 5544 z^5 - 5544 z^(11/2) + 1848 z^6 + 1848 z^(13/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-2048 + 8928 z - 13995 z^2 + 7885 z^3 + 1155 z^4 - 2849 z^5 + 924 z^6) 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]