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http://functions.wolfram.com/01.08.06.0004.02
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Tan[z] \[Proportional] -(1/(z - Pi/2)) + (1/3) (z - Pi/2) +
(1/45) (z - Pi/2)^3 + (2/945) (z - Pi/2)^5 + \[Ellipsis] /; (z -> Pi/2)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Tan", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]]]]], "+", RowBox[List[FractionBox["1", "3"], RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "45"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "3"]]], "+", RowBox[List[FractionBox[RowBox[List["2", " "]], "945"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "5"]]], "+", "\[Ellipsis]"]]]], "/;", " ", RowBox[List["(", RowBox[List["z", "\[Rule]", FractionBox["\[Pi]", "2"]]], ")"]]]]]]
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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> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 45 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mtext> </mtext> </mrow> <mn> 945 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <tan /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 45 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 2 <sep /> 945 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tan", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]]]]], "+", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "45"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "3"]]], "+", RowBox[List[FractionBox["2", "945"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "5"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", FractionBox["\[Pi]", "2"]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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