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   http://functions.wolfram.com/09.51.06.0004.01
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    ModularLambda[z] == (1 + 2 Sum[(-1)^k/E^((I k^2 Pi)/z), {k, 1, Infinity}])^4/
  (1 + 2 Sum[E^(-((I k^2 Pi)/z)), {k, 1, Infinity}])^4 
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   Cell[BoxData[RowBox[List[RowBox[List["ModularLambda", "[", "z", "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["k", "2"], " ", "\[Pi]"]], "z"]]]]]]]]]]]], ")"]], "4"], "/", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["k", "2"], " ", "\[Pi]"]], "z"]]]]]]]]]], ")"]], "4"]]]]]]] 
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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>  <semantics>  <mrow>  <mi> λ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Lambda]", "(", TagBox["z", Identity, Rule[Editable, True], Rule[Selectable, True]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation>  </semantics>  <mo>  </mo>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> ∞ </mi>  </munderover>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mi> k </mi>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <msup>  <mi> k </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  <mi> z </mi>  </mfrac>  </mrow>  </msup>  </mrow>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 4 </mn>  </msup>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> ∞ </mi>  </munderover>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <msup>  <mi> k </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mi> π </mi>  </mrow>  <mi> z </mi>  </mfrac>  </mrow>  </msup>  </mrow>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 4 </mn>  </msup>  </mfrac>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> ModularLambda </ci>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <infinity />  </uplimit>  <apply>  <times />  <apply>  <power />  <cn type='integer'> -1 </cn>  <ci> k </ci>  </apply>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <apply>  <power />  <ci> k </ci>  <cn type='integer'> 2 </cn>  </apply>  <pi />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> 4 </cn>  </apply>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <infinity />  </uplimit>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <apply>  <power />  <ci> k </ci>  <cn type='integer'> 2 </cn>  </apply>  <pi />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 4 </cn>  </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["ModularLambda", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["k", "2"], " ", "\[Pi]"]], "z"]]]]]]]]]]]], ")"]], "4"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["k", "2"], " ", "\[Pi]"]], "z"]]]]]]]]]], ")"]], "4"]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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