Meijer G-function: Integral transforms (formula 07.34.22.0002)

MeijerG

$Mathematica Notation$

Hypergeometric Functions

MeijerG[{{a₁,...,a_n},{a_n+1,...,a_p}},{{b₁,...,b_m},{b_m+1,...,b_q}},z]

Integral transforms

Fourier sin transforms

http://functions.wolfram.com/07.34.22.0002.01

Input Form

FourierSinTransform[t^(\[Alpha] - 1) MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, \[Omega] t^((2 l)/k)], t, z] == ((k^\[Mu] (2 l)^(\[Alpha] - 1/2))/(z^\[Alpha] (2 Pi)^(SuperStar[c] (k - 1)))) MeijerG[{{(1 - \[Alpha])/(2 l), \[Ellipsis], ((-1 - \[Alpha])/2 + l)/l, Subscript[a, 1]/k, \[Ellipsis], (Subscript[a, 1] + k - 1)/k, \[Ellipsis], Subscript[a, n]/k, \[Ellipsis], (Subscript[a, n] + k - 1)/ k}, {Subscript[a, n + 1]/k, \[Ellipsis], (Subscript[a, n + 1] + k - 1)/ k, \[Ellipsis], Subscript[a, p]/k, \[Ellipsis], (Subscript[a, p] + k - 1)/k, (1 - \[Alpha]/2)/l, \[Ellipsis], (l - \[Alpha]/2)/l}}, {{Subscript[b, 1]/k, \[Ellipsis], (Subscript[b, 1] + k - 1)/k, \[Ellipsis], Subscript[b, m]/k, \[Ellipsis], (Subscript[b, m] + k - 1)/k}, {Subscript[b, m + 1]/k, \[Ellipsis], (Subscript[b, m + 1] + k - 1)/k, \[Ellipsis], Subscript[b, q]/k, \[Ellipsis], (Subscript[b, q] + k - 1)/k}}, (\[Omega]^k (2 l)^(2 l))/(z^(2 l) k^(k (q - p)))] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && GCD[k, l] == 1 && (\[DoubleStruckCapitalC]\[DoubleStruckCapitalC] /; \[Alpha] -> \[Alpha]/2 && \[Sigma] == z^2/4 && s == 1 && t == u == Subscript[d, 2] == 0 && v == 2 && Subscript[d, 1] == 1/2)

Standard Form

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MathML Form

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</mn> </mfrac> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

MeijerG[{{a₁,...,a_n},{a_n+1,...,a_p}},{{b₁,...,b_m},{b_m+1,...,b_q}},z,r]