|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.02.20.0009.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D[EllipticTheta[2, z, q], q] ==
(-(1/(4 q))) (EllipticThetaPrime[1, z, q]/EllipticTheta[1, z, q] -
EllipticTheta[2, 0, q]^2 ((EllipticTheta[3, z, q] EllipticTheta[4, z,
q])/(EllipticTheta[1, z, q] EllipticTheta[2, z, q])))^2
EllipticTheta[2, z, q] + (1/(4 q)) EllipticTheta[3, 0, q]^2
EllipticTheta[4, 0, q]^2 (EllipticTheta[1, z, q]^2/
EllipticTheta[2, z, q]) + (1/(q Pi^2)) EllipticTheta[2, z, q]
(WeierstrassZeta[1, WeierstrassInvariants[{1, Log[q]/(Pi I)}]] +
(Pi^2/12) (EllipticTheta[3, 0, q]^4 + EllipticTheta[4, 0, q]^4))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "q"], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", " ", "q"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]], "-", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], "2"], FractionBox[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "z", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]], RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]]]]]], ")"]], "2"], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["4", " ", "q"]]], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "2"], SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "2"], FractionBox[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "2"], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]], "+", RowBox[List[FractionBox["1", RowBox[List["q", " ", SuperscriptBox["\[Pi]", "2"]]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]], RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["1", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["Log", "[", "q", "]"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], "}"]], "]"]]]], "]"]], "+", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "12"], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "4"]]], ")"]]]]]], ")"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> q </mi> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> q </mi> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msubsup> <semantics> <mi> ϑ </mi> <annotation encoding='Mathematica'> TagBox["\[CurlyTheta]", EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mrow> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <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> </mrow> </mrow> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mn> 1 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> q </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mfrac> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> q </mi> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 12 </mn> </mfrac> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> + </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox["1", Identity, Rule[Editable, True], Rule[Selectable, True]], ";", RowBox[List[SubscriptBox["g", "2"], "(", RowBox[List["1", ",", FractionBox[RowBox[List["log", "(", "q", ")"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]], ",", RowBox[List[SubscriptBox["g", "3"], "(", RowBox[List["1", ",", FractionBox[RowBox[List["log", "(", "q", ")"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]], Rule[Editable, True], Rule[Selectable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> q </mi> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> q </mi> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msubsup> <semantics> <mi> ϑ </mi> <annotation encoding='Mathematica'> TagBox["\[CurlyTheta]", EllipticThetaPrime] </annotation> </semantics> <mn> 1 </mn> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mrow> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mfrac> <mrow> <mtext> </mtext> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <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> </mrow> </mrow> <mrow> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mtext> </mtext> <mn> 1 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> q </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mfrac> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> q </mi> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 12 </mn> </mfrac> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> + </mo> <msup> <mrow> <msub> <mi> ϑ </mi> <mn> 4 </mn> </msub> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> ; </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> q </mi> <mo> ) </mo> </mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox["1", Identity, Rule[Editable, True], Rule[Selectable, True]], ";", RowBox[List[SubscriptBox["g", "2"], "(", RowBox[List["1", ",", FractionBox[RowBox[List["log", "(", "q", ")"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]], ",", RowBox[List[SubscriptBox["g", "3"], "(", RowBox[List["1", ",", FractionBox[RowBox[List["log", "(", "q", ")"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], ")"]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]], Rule[Editable, True], Rule[Selectable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["q_"]]], RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["EllipticThetaPrime", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "0", ",", "q"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "z", ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "z", ",", "q"]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]]]], ")"]], "2"], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]], RowBox[List["4", " ", "q"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["1", ",", "z", ",", "q"]], "]"]], "2"]]], RowBox[List[RowBox[List["(", RowBox[List["4", " ", "q"]], ")"]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", "z", ",", "q"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List["1", ",", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["Log", "[", "q", "]"]], RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]], "}"]], "]"]]]], "]"]], "+", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["3", ",", "0", ",", "q"]], "]"]], "4"], "+", SuperscriptBox[RowBox[List["EllipticTheta", "[", RowBox[List["4", ",", "0", ",", "q"]], "]"]], "4"]]], ")"]]]]]], ")"]]]], RowBox[List["q", " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|