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http://functions.wolfram.com/01.02.23.0007.01
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Sum[q^(k^2 + k), {k, 0, Infinity}] == (1/(2 q^(1/4))) EllipticTheta[2, 0, q]
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], SuperscriptBox["q", RowBox[List[SuperscriptBox["k", "2"], "+", "k"]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox["q", RowBox[List["1", "/", "4"]]]]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]]]]]]]]
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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> <msup> <mi> q </mi> <mrow> <msup> <mi> k </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mi> k </mi> </mrow> </msup> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mroot> <mi> q </mi> <mn> 4 </mn> </mroot> </mrow> </mfrac> </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> <power /> <ci> q </ci> <apply> <plus /> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <ci> k </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> q </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]"], SuperscriptBox["q_", RowBox[List[SuperscriptBox["k_", "2"], "+", "k_"]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], RowBox[List["2", " ", SuperscriptBox["q", RowBox[List["1", "/", "4"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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