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http://functions.wolfram.com/01.07.23.0020.01
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Sum[(z^k Cos[k x])/k!, {k, 0, Infinity}] == E^(z Cos[x]) Cos[z Sin[x]]
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["z", "k"], " ", RowBox[List["Cos", "[", RowBox[List["k", " ", "x"]], "]"]]]], RowBox[List["k", "!"]]]]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", RowBox[List["Cos", "[", "x", "]"]]]]], " ", RowBox[List["Cos", "[", RowBox[List["z", " ", RowBox[List["Sin", "[", "x", "]"]]]], "]"]]]]]]]]
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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> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mrow> <msup> <mi> z </mi> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> ⁢ </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <cos /> <apply> <times /> <ci> k </ci> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> z </ci> <apply> <cos /> <ci> x </ci> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> z </ci> <apply> <sin /> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["z_", "k_"], " ", RowBox[List["Cos", "[", RowBox[List["k_", " ", "x_"]], "]"]]]], RowBox[List["k_", "!"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["z", " ", RowBox[List["Cos", "[", "x", "]"]]]]], " ", RowBox[List["Cos", "[", RowBox[List["z", " ", RowBox[List["Sin", "[", "x", "]"]]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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