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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] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.34.20.0015.02









  


  








Input Form





D[z^(a - 1) MeijerG[{{a, Subscript[a, 2], \[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]}}, 1/z], {z, u}] == (-1)^u z^(a - u - 1) MeijerG[{{a - u, Subscript[a, 2], \[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]}}, 1/z] /; Element[u, Integers] && u >= 0








Standard Form





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MathML Form







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</mo> <mrow> <mi> u </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "u_"]], "}"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["z_", RowBox[List["a_", "-", "1"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", SubscriptBox["a_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "n_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a_", RowBox[List["n_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "m_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", RowBox[List["m_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]]]], "}"]], ",", FractionBox["1", "z_"]]], "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "u"], " ", SuperscriptBox["z", RowBox[List["a", "-", "u", "-", "1"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "-", "u"]], ",", SubscriptBox["aa", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["bb", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]]]], "}"]], ",", FractionBox["1", "z"]]], "]"]]]], "/;", RowBox[List[RowBox[List["u", "\[Element]", "Integers"]], "&&", RowBox[List["u", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29