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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] > Series representations > Generalized power series > Expansions at z==0 > Case of simple poles





http://functions.wolfram.com/07.34.06.0003.01









  


  








Input Form





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]}}, z] == Sum[GammaResidue[{{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {1 - Subscript[a, 1], \[Ellipsis], 1 - Subscript[a, n]}}, {{Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}, {1 - Subscript[b, m + 1], \[Ellipsis], 1 - Subscript[b, q]}}, {Subscript[b, k], 1, i}, z], {k, 1, m}, {i, 0, Infinity}] /; (p < q || (p == q && Abs[z] < 1)) && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= m && 1 <= k <= m, !Element[Subscript[b, j] - Subscript[b, k], Integers]]








Standard Form





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MathML Form







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</mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> <mo> &#8743; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> j </mi> <mo> &#8804; </mo> <mi> m </mi> </mrow> <mo> &#8743; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> k </mi> <mo> &#8804; </mo> <mi> m </mi> </mrow> </mrow> </mrow> </msub> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> b </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> k </mi> </msub> </mrow> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29