|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.29.27.1449.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ArcCsch[z] == I (Pi/2 - (Sqrt[1 + I/z]/Sqrt[-(I/z) - 1]) ArcCosh[-(I/z)])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["ArcCsch", "[", "z", "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", RowBox[List["(", " ", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "z"]]]], " "]], SqrtBox[RowBox[List[RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]], "-", "1"]]]], RowBox[List["ArcCosh", "[", RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]], "]"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> csch </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mi> z </mi> </mfrac> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mi> z </mi> </mfrac> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <msup> <mi> cosh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mi> ⅈ </mi> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccsch /> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccosh /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", FractionBox["\[ImaginaryI]", "z"]]]], " ", RowBox[List["ArcCosh", "[", RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["-", FractionBox["\[ImaginaryI]", "z"]]], "-", "1"]]]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|