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http://functions.wolfram.com/09.04.06.0006.01
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Log[EllipticTheta[4, z, q]] == Log[EllipticTheta[4, 0, q]] +
4 Sum[(1/r) (q^r/(1 - q^(2 r))) Sin[r z]^2, {r, 1, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "]"]], "+", RowBox[List["4", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["r", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox["1", "r"], " ", FractionBox[SuperscriptBox["q", "r"], RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", "r"]]]]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]], "2"]]]]]]]]]]]]]
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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> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mfrac> <msup> <mi> q </mi> <mi> r </mi> </msup> <mrow> <mi> r </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> q </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> r </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ln /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <sum /> <bvar> <ci> r </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <ci> q </ci> <ci> r </ci> </apply> <apply> <power /> <apply> <times /> <ci> r </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "]"]], "+", RowBox[List["4", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["r", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["q", "r"], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["r", " ", "z"]], "]"]], "2"]]], RowBox[List["r", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", " ", "r"]]]]], ")"]]]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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