Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ae4x)

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=-9/4, b>=a

For fixed z and a=-9/4, b=-3/4

http://functions.wolfram.com/07.23.03.ae4x.01

Input Form

Hypergeometric2F1[-(9/4), -(3/4), 5, z] == -((1/(2546168625 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] (2 (576 - 5592 z + 27045 z^2 - 104580 z^3 - 716450 z^4 - 122892 z^5 + 4389 z^6) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-1152 + 1152 Sqrt[z] + 10320 z - 10320 z^(3/2) - 46485 z^2 + 46485 z^(5/2) + 175455 z^3 - 175455 z^(7/2) + 316225 z^4 - 316225 z^(9/2) + 4389 z^5 - 4389 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]