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http://functions.wolfram.com/01.19.16.0119.01
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Sinh[z] - I Sin[z] == 2 Cosh[(z E^((I Pi)/4))/Sqrt[2]]
Sinh[z/(E^((I Pi)/4) Sqrt[2])]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sinh", "[", "z", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sin", "[", "z", "]"]]]]]], "\[Equal]", RowBox[List["2", " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]]], SqrtBox["2"]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]]]]], SqrtBox["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> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mn> 4 </mn> </mfrac> </msup> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cosh /> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <times /> <imaginaryi /> <pi /> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sinh", "[", "z_", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sin", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "4"]]]], SqrtBox["2"]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], ")"]]]]]]], SqrtBox["2"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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