WeierstrassZeta[z t, {Subscript[g, 2], Subscript[g, 3]}] == (1/t) WeierstrassZeta[z, {Subscript[g, 2] t^4, Subscript[g, 3] t^6}] /; Element[t, Reals]

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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> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[&quot;z&quot;, &quot; &quot;, &quot;t&quot;]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> t </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 4 </mn> </msup> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;2&quot;], &quot; &quot;, SuperscriptBox[&quot;t&quot;, &quot;4&quot;]]], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> t </mi> <mn> 6 </mn> </msup> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[&quot;g&quot;, &quot;3&quot;], &quot; &quot;, SuperscriptBox[&quot;t&quot;, &quot;6&quot;]]], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> t </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassZeta </ci> <apply> <times /> <ci> z </ci> <ci> t </ci> </apply> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> t </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Zeta </ci> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> t </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29