Hyperbolic cosine integral: Transformations (formula 01.20.16.0002)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Transformations

Transformations and argument simplifications

Argument involving basic arithmetic operations

http://functions.wolfram.com/01.20.16.0002.01

Input Form

Cosh[a (b z^c)^m] == Cosh[a b^m z^(m c)] /; Element[2 m, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "c"]]], ")"]], "m"]]], "]"]], "\[Equal]", RowBox[List["Cosh", "[", RowBox[List["a", " ", SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], "]"]]]], "/;", RowBox[List["Element", "[", RowBox[List[RowBox[List["2", " ", "m"]], ",", "Integers"]], "]"]]]]]]

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> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> c </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> b </mi> <mi> m </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> ∈ </mo> <mi> ℤ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <cosh /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <ci> c </ci> </apply> </apply> <ci> m </ci> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> b </ci> <ci> m </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <ci> c </ci> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> <ci> ℤ </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", RowBox[List["a_", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b_", " ", SuperscriptBox["z_", "c_"]]], ")"]], "m_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", " ", SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], "]"]], "/;", RowBox[List[RowBox[List["2", " ", "m"]], "\[Element]", "Integers"]]]]]]]]

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

2001-10-29