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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/01.30.06.0045.01









  


  










Input Form





ArcSech[z] \[Proportional] ((Sqrt[1 - Subscript[z, 0]] Sqrt[Subscript[z, 0]])/ Sqrt[-1 + Subscript[z, 0]]) Sqrt[1/Subscript[z, 0]] (Subscript[z, 0]/(1 - Subscript[z, 0]))^ ((1/2) Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)]) ((1 - Subscript[z, 0])/Subscript[z, 0])^ ((1/2) Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)]) (-2 Pi I I^Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)] Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)] Floor[(Pi + Arg[(1 + Subscript[z, 0])/Subscript[z, 0]])/(2 Pi)] + (Subscript[z, 0]/(1 + Subscript[z, 0]))^ ((1/2) Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)]) ((1 + Subscript[z, 0])/Subscript[z, 0])^ ((1/2) Floor[Arg[(Subscript[z, 0] - z)/(z Subscript[z, 0])]/(2 Pi)]) ArcSec[Subscript[z, 0]]) (1 + O[z - Subscript[z, 0]])










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <arcsec /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSech", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", SubscriptBox["zz", "0"]]]], " ", SqrtBox[SubscriptBox["zz", "0"]]]], ")"]], " ", SqrtBox[FractionBox["1", SubscriptBox["zz", "0"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["zz", "0"], RowBox[List["1", "-", SubscriptBox["zz", "0"]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", SubscriptBox["zz", "0"]]], SubscriptBox["zz", "0"]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[Pi]", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ImaginaryI]", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", FractionBox[RowBox[List["1", "+", SubscriptBox["zz", "0"]]], SubscriptBox["zz", "0"]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["zz", "0"], RowBox[List["1", "+", SubscriptBox["zz", "0"]]]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "+", SubscriptBox["zz", "0"]]], SubscriptBox["zz", "0"]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], RowBox[List["z", " ", SubscriptBox["zz", "0"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", RowBox[List["ArcSec", "[", SubscriptBox["zz", "0"], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["zz", "0"]]]]]]]]]










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





2007-05-02





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