|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.01.18.0073.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
EllipticTheta[1, a + b, q] EllipticTheta[1, a - b, q]
EllipticTheta[1, c + d, q] EllipticTheta[1, c - d, q] +
EllipticTheta[1, a + c, q] EllipticTheta[1, a - c, q]
EllipticTheta[1, d + b, q] EllipticTheta[1, d - b, q] +
EllipticTheta[1, a + d, q] EllipticTheta[1, a - d, q]
EllipticTheta[1, b + c, q] EllipticTheta[1, b - c, q] == 0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "+", "b"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "-", "b"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["c", "+", "d"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["c", "-", "d"]], ",", "q"]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "+", "c"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "-", "c"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["d", "+", "b"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["d", "-", "b"]], ",", "q"]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "+", "d"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a", "-", "d"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["b", "+", "c"]], ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["b", "-", "c"]], ",", "q"]], "]"]]]]]], "\[Equal]", "0"]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> + </mo> <mi> d </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> d </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> d </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> d </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> + </mo> <mi> d </mi> </mrow> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> b </ci> <ci> d </ci> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> <ci> q </ci> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <ci> d </ci> </apply> <ci> q </ci> </apply> </apply> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <ci> c </ci> <ci> d </ci> </apply> <ci> q </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "+", "b_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "-", "b_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["c_", "+", "d_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["c_", "-", "d_"]], ",", "q_"]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "+", "c_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "-", "c_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["d_", "+", "b_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["d_", "-", "b_"]], ",", "q_"]], "]"]]]], "+", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "+", "d_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["a_", "-", "d_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["b_", "+", "c_"]], ",", "q_"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", RowBox[List["b_", "-", "c_"]], ",", "q_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|