EllipticThetaPrime[1, \[Nu], q] EllipticTheta[i + 1, \[Nu], q] - EllipticTheta[1, \[Nu], q] EllipticThetaPrime[i + 1, \[Nu], q] == EllipticTheta[i + 1, 0, q]^2 EllipticTheta[j + 1, \[Nu], q] EllipticTheta[k + 1, \[Nu], q] /; Element[{i, j, k}, {1, 2, 3}] && i != j != k

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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> <mrow> <mrow> <mrow> <msubsup> <mi> &#977; </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msub> <mi> &#977; </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> &#8242; </mo> </msubsup> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> i </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> j </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> i </mi> <mo> , </mo> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> i </mi> <mo> &#8800; </mo> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> &#957; </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#957; </ci> <ci> q </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> &#957; </ci> <ci> q </ci> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> &#977; </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <ci> &#957; </ci> <ci> q </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#957; </ci> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#957; </ci> <ci> q </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </ci> <ci> k </ci> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29