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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Products > Infinite products





http://functions.wolfram.com/01.02.24.0004.01









  


  








Input Form





Product[(1 - q^k)/(1 + q^k), {k, 1, Infinity}] == EllipticTheta[4, 0, q]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "-", SuperscriptBox["q", "k"]]], RowBox[List["1", "+", SuperscriptBox["q", "k"]]]]]], "\[Equal]", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]]]]]]








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> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mi> k </mi> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> q </mi> <mi> k </mi> </msup> </mrow> </mfrac> </mrow> <mo> &#10869; </mo> <mrow> <msub> <mi> &#977; </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> q </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> q </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k_", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["1", "-", SuperscriptBox["q_", "k_"]]], RowBox[List["1", "+", SuperscriptBox["q_", "k_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]]]]]]


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





2001-10-29