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variants of this functions
Erf




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z1,z2] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/06.26.26.0006.01









  


  








Input Form





Erf[Sqrt[Subscript[z, 1]], Sqrt[Subscript[z, 2]]] == (1/Sqrt[Pi]) (MeijerG[{{1}, {}}, {{1/2}, {0}}, Subscript[z, 2]] - MeijerG[{{1}, {}}, {{1/2}, {0}}, Subscript[z, 1]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Erf", "[", RowBox[List[SqrtBox[SubscriptBox["z", "1"]], ",", SqrtBox[SubscriptBox["z", "2"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1", " "]], SqrtBox["\[Pi]"]], RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", SubscriptBox["z", "2"]]], "]"]], "-", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", SubscriptBox["z", "1"]]], "]"]]]], ")"]]]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erf", "[", RowBox[List[SqrtBox[SubscriptBox["z_", "1"]], ",", SqrtBox[SubscriptBox["z_", "2"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", SubscriptBox["zz", "2"]]], "]"]], "-", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", SubscriptBox["zz", "1"]]], "]"]]]], SqrtBox["\[Pi]"]]]]]]


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





2001-10-29