Inverse hyperbolic sine: Specific values (formula 01.25.03.0007)

ArcSinh

$Mathematica Notation$

Elementary Functions

Specific values

Values at fixed points

http://functions.wolfram.com/01.25.03.0007.01

Input Form

ArcSinh[-((I Sqrt[2 - Sqrt[2]])/2)] == -((Pi I)/8)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["ArcSinh", "[", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", SqrtBox[RowBox[List["2", "-", SqrtBox["2"]]]]]], "2"]]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> - </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mn> 8 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsinh /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["2", "-", SqrtBox["2"]]]]]], ")"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]]]

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

2001-10-29