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variants of this functions
MeijerG




Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Integral transforms > Hilbert transform





http://functions.wolfram.com/07.34.22.0009.01









  


  








Input Form





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








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)





2001-10-29