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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] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > Representation of fundamental system solutions near point z==(-1)m+n-p for p==q in the general case





http://functions.wolfram.com/07.34.13.0002.01









  


  










Input Form





(-1)^(m + n - q) z Fold[Function[{f, l}, z D[f, z] + (1 - Subscript[a, l]) f], w[z], {1, \[Ellipsis], q}] - Fold[Function[{f, k}, z D[f, z] - Subscript[b, k] f], w[z], {1, \[Ellipsis], q}] == 0 /; (w[z] == Subscript[c, j] MeijerG[{{}, {Subscript[a, 1], \[Ellipsis], Subscript[a, q]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, {}}, z] + Sum[Subscript[c, h] (1 - KroneckerDelta[h - j]) MeijerG[{{Subscript[b, h], Subscript[b, j], Subscript[a, 1], \[Ellipsis], Subscript[a, q]}, {}}, {{Subscript[b, h], Subscript[b, j]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}}, z], {h, 1, q}] /; 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] && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= q && 1 <= k <= q, !Element[Subscript[b, j] - Subscript[b, k], Integers]] && 1 <= j <= q)










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> &lt; </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; 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Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.