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http://functions.wolfram.com/01.07.16.0159.01
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Cos[a (b z^c)^m] == Cos[a b^m z^(m c)] /; Inequality[-Pi, Less,
Arg[b] + Im[c Log[z]], LessEqual, Pi]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List["a", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["z", "c"]]], ")"]], "m"]]], "]"]], "\[Equal]", RowBox[List["Cos", "[", RowBox[List["a", " ", SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[RowBox[List["Arg", "[", "b", "]"]], "+", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]
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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> cos </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> cos </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> <mo> - </mo> <mi> π </mi> </mrow> <mo> < </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ≤ </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <cos /> <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> <cos /> <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> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <plus /> <apply> <arg /> <ci> b </ci> </apply> <apply> <imaginary /> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> <leq /> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cos", "[", RowBox[List["a_", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b_", " ", SuperscriptBox["z_", "c_"]]], ")"]], "m_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Cos", "[", RowBox[List["a", " ", SuperscriptBox["b", "m"], " ", SuperscriptBox["z", RowBox[List["m", " ", "c"]]]]], "]"]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[RowBox[List["Arg", "[", "b", "]"]], "+", RowBox[List["Im", "[", RowBox[List["c", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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