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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 > Main terms of asymptotic expansions > Expansions at z==(-1)m+n-q for p==q





http://functions.wolfram.com/07.34.06.0043.01









  


  










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] \[Proportional] c (1 + O[z - (-1)^(m + n - q)]) + d Log[1 - (-1)^(q - m - n) z] (1 + O[z - (-1)^(m + n - q)]) /; (z -> (-1)^(m + n - q)) && Abs[z] < 1 && Subscript[\[Psi], q] == Sum[Subscript[a, j] - Subscript[b, j], {j, 1, q}] - 1 && c == 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]}}, (-1)^(m + n - q)] && d == (-Pi^(m + n - q - 1)) Sum[(Product[Sin[(Subscript[a, k] - Subscript[b, h]) Pi], {k, n + 1, q}]/ Product[If[k == h, 1, Sin[(Subscript[b, k] - Subscript[b, h]) Pi]], {k, 1, m}]) E^((m + n - q) Pi I Subscript[b, h]), {h, 1, m}] && Subscript[\[Psi], q] == 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





© 1998- Wolfram Research, Inc.