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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] > Specific values > Specialized values > Cases with arbitrary {m,n,p,q} > Case {m,n,p,q}={1,n,n,n+1}





http://functions.wolfram.com/07.34.03.0034.01









  


  








Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {}}, {{0}, {Subscript[a, 1] + 1, \[Ellipsis], Subscript[a, n] + 1}}, z] == Sum[((-1)^k/(k + 1)!) Sum[(-1)^j Binomial[k + 1, j + 1] (j + 1)^(n + 1) (-z)^k, {j, 0, k}], {k, 0, n}]/E^z /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n] == -1








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "n_"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a_", "1"], "+", "1"]], ",", "\[Ellipsis]_", ",", RowBox[List[SubscriptBox["a_", "n_"], "+", "1"]]]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["k", "+", "1"]], ",", RowBox[List["j", "+", "1"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["j", "+", "1"]], ")"]], RowBox[List["n", "+", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], "k"]]]]]]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "!"]]]]]]], "/;", RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", "n"], "\[Equal]", RowBox[List["-", "1"]]]]]]]]]]


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





2001-10-29