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http://functions.wolfram.com/01.18.06.0062.01
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ArcSec[z]^2 \[Proportional] Pi^2/4 - Pi/z + 1/z^2 - Pi/(6 z^3) +
\[Ellipsis] /; Abs[z] -> Infinity
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["ArcSec", "[", "z", "]"]], "2"], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "-", FractionBox["\[Pi]", "z"], "+", FractionBox["1", SuperscriptBox["z", "2"]], "-", FractionBox["\[Pi]", RowBox[List["6", " ", SuperscriptBox["z", "3"]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["Abs", "[", "z", "]"]]]], "\[Rule]", "\[Infinity]"]]]]
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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> <mrow> <msup> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ∝ </mo> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> <mo> - </mo> <mfrac> <mi> π </mi> <mi> z </mi> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> - </mo> <mfrac> <mi> π </mi> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Rule </ci> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <power /> <apply> <arcsec /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <abs /> <ci> z </ci> </apply> </apply> <infinity /> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["ArcSec", "[", "z", "]"]], "2"], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "-", FractionBox["\[Pi]", "z"], "+", FractionBox["1", SuperscriptBox["z", "2"]], "-", FractionBox["\[Pi]", RowBox[List["6", " ", SuperscriptBox["z", "3"]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["Abs", "[", "z", "]"]]]], "\[Rule]", "\[Infinity]"]]]] |
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Date Added to functions.wolfram.com (modification date)
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