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http://functions.wolfram.com/01.06.08.0002.01
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Sin[z] == z Product[If[k == 0, 1, (1 - z/(Pi k)) E^(z/(Pi k))],
{k, -Infinity, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["Sin", "[", "z", "]"]], "\[Equal]", RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List["k", "\[Equal]", "0"]], ",", "1", ",", RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox["z", RowBox[List["\[Pi]", " ", "k"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox["z", RowBox[List["\[Pi]", " ", "k"]]]]]]]], "]"]]]]]]]]]]
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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> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <munder> <mrow> <mi> k </mi> <mo> = </mo> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> </mrow> <mrow> <mi> k </mi> <mo> ≠ </mo> <mn> 0 </mn> </mrow> </munder> <mi> ∞ </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> z </mi> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mfrac> <mi> z </mi> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mfrac> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> sin </ms> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> UnderoverscriptBox </ci> <ms> ∏ </ms> <apply> <ci> UnderscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> ∞ </ms> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> ≠ </ms> <ms> 0 </ms> </list> </apply> </apply> <ms> ∞ </ms> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <apply> <ci> FractionBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> π </ms> <ms> k </ms> </list> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SuperscriptBox </ci> <ms> ⅇ </ms> <apply> <ci> FractionBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> π </ms> <ms> k </ms> </list> </apply> </apply> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sin", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List["k", "\[Equal]", "0"]], ",", "1", ",", RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox["z", RowBox[List["\[Pi]", " ", "k"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox["z", RowBox[List["\[Pi]", " ", "k"]]]]]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
