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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==(-1)m+n-q for p==q > The general formula for psiqZ in the particular case |z|>1





http://functions.wolfram.com/07.34.06.0009.01









  


  










Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, q]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z] == (-(Pi^(m + n - q)/Sin[Subscript[\[Psi], q] Pi])) Sum[z^(Subscript[a, h] - 1) ((-1)^(q - m - n) z)^(1 - Subscript[a, h]) (Product[Sin[(Subscript[a, h] - Subscript[b, k]) Pi], {k, m + 1, q}]/ Product[If[k == h, 1, Sin[(Subscript[a, h] - Subscript[a, k]) Pi]], {k, 1, n}]) (MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, q]}, {}}, {{}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}}, (-1)^(q - m - n) z] - (1/Pi^2) Sum[Sin[(Subscript[a, h] - Subscript[a, j]) Pi] (Product[Sin[(Subscript[b, k] - Subscript[a, j]) Pi], {k, 1, q}]/ Product[If[k == j, 1, Sin[(Subscript[a, k] - Subscript[a, j]) Pi]], {k, 1, q}]) MeijerG[{{Subscript[a, h], Subscript[a, j]}, {Subscript[a, 1], \[Ellipsis], Subscript[a, q]}}, {{Subscript[a, h], Subscript[a, j], Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, {}}, (-1)^(q - m - n) z], {j, 1, q}]), {h, 1, n}] /; Abs[z] > 1 && (Subscript[\[Psi], q] == -\[Mu] == Sum[Subscript[a, j] - Subscript[b, j], {j, 1, q}] - 1 /; p == q) && !Element[Subscript[\[Psi], q], Integers] && m n != 0










Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &gt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#968; </mi> <mi> q </mi> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> p </mi> <mo> &#10869; </mo> <mi> q </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#968; </mi> <mi> q </mi> </msub> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29