Erf[Subscript[z, 1], Subscript[z, 2]] \[Proportional] (2/Sqrt[Pi]) (Subscript[z, 2] - Subscript[z, 2]^3/3 + Subscript[z, 2]^5/10 - O[Subscript[z, 2]^7]) - (2/Sqrt[Pi]) (Subscript[z, 1] - Subscript[z, 1]^3/3 + Subscript[z, 1]^5/10 - O[Subscript[z, 1]^7])

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mfrac> <mn> 2 </mn> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 5 </mn> </msubsup> <mn> 10 </mn> </mfrac> <mo> - </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 7 </mn> </msubsup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 2 </mn> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mn> 3 </mn> </mfrac> <mo> + </mo> <mfrac> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 5 </mn> </msubsup> <mn> 10 </mn> </mfrac> <mo> - </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 7 </mn> </msubsup> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> Erf </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Erf", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "-", FractionBox[SubsuperscriptBox["zz", "2", "3"], "3"], "+", FractionBox[SubsuperscriptBox["zz", "2", "5"], "10"], "-", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "2"], "]"]], "7"]]], ")"]]]], SqrtBox["\[Pi]"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[SubscriptBox["zz", "1"], "-", FractionBox[SubsuperscriptBox["zz", "1", "3"], "3"], "+", FractionBox[SubsuperscriptBox["zz", "1", "5"], "10"], "-", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "1"], "]"]], "7"]]], ")"]]]], SqrtBox["\[Pi]"]]]]]]]]

2007-05-02