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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Summation > Finite summation





http://functions.wolfram.com/01.06.23.0005.01









  


  








Input Form





Sum[Sin[(2 k - 1) a], {k, 1, n}] == Csc[a] Sin[a n]^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "1"]], ")"]], " ", "a"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Csc", "[", "a", "]"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["a", " ", "n"]], "]"]], "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> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <sin /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <apply> <csc /> <ci> a </ci> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> a </ci> <ci> n </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k_"]], "-", "1"]], ")"]], " ", "a_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Csc", "[", "a", "]"]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["a", " ", "n"]], "]"]], "2"]]]]]]]


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





2001-10-29