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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,r] > Primary definition





http://functions.wolfram.com/07.35.02.0001.01









  


  










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, r] == (1/(2 Pi I)) ContourIntegrate[ (Product[Gamma[Subscript[b, k] + s], {k, 1, m}] Product[Gamma[1 - Subscript[a, k] - s], {k, 1, n}])/ (Product[Gamma[Subscript[a, k] + s], {k, n + 1, p}] Product[Gamma[1 - Subscript[b, k] - s], {k, m + 1, q}])/z^(s/r), {s, \[ScriptCapitalL]}] /; Element[r, Reals] && r != 0 && Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && Element[p, Integers] && p >= 0 && Element[q, Integers] && q >= 0 && m <= q && n <= p










Standard Form





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MathML Form







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</mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> r </mi> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &#8804; </mo> <mi> q </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8804; </mo> <mi> p </mi> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29