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ArcCosh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/01.26.13.0001.01









  


  








Input Form





Sqrt[z - 1] Sqrt[z + 1] Derivative[1][w][z] == 1 /; w[z] == ArcCosh[z] && w[0] == (I Pi)/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SqrtBox[RowBox[List["z", "-", "1"]]], " ", SqrtBox[RowBox[List["z", "+", "1"]]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "\[Equal]", "1"]], "/;", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["ArcCosh", "[", "z", "]"]]]], "\[And]", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> cosh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <arccosh /> <ci> z </ci> </apply> </apply> <apply> <eq /> <apply> <ci> w </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <imaginaryi /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SqrtBox[RowBox[List["z_", "-", "1"]]], " ", SqrtBox[RowBox[List["z_", "+", "1"]]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "/;", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["ArcCosh", "[", "z", "]"]]]], "&&", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "2"]]]]]]]]]]]


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





2001-10-29