|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/09.51.20.0005.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D[ModularLambda[z], {z, 5}] == (-(1/Pi^5)) 512 I
EllipticK[ModularLambda[z]]^6 (-1 + ModularLambda[z]) ModularLambda[z]
(15 EllipticE[ModularLambda[z]]^4 - 60 EllipticE[ModularLambda[z]]^3
EllipticK[ModularLambda[z]] ModularLambda[z] +
30 EllipticE[ModularLambda[z]]^2 EllipticK[ModularLambda[z]]^2
(1 + ModularLambda[z]) (-1 + 2 ModularLambda[z]) -
10 EllipticE[ModularLambda[z]] EllipticK[ModularLambda[z]]^3
(1 + ModularLambda[z]) (-2 + ModularLambda[z] + 2 ModularLambda[z]^2) +
EllipticK[ModularLambda[z]]^4 (-3 - 4 ModularLambda[z] +
ModularLambda[z]^2 + 6 ModularLambda[z]^3 + 2 ModularLambda[z]^4))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "5"]], "}"]]], RowBox[List["ModularLambda", "[", "z", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", SuperscriptBox["\[Pi]", "5"]]]], "512", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "6"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["ModularLambda", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "4"]]], " ", "-", RowBox[List["60", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "3"], " ", RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], RowBox[List["ModularLambda", "[", "z", "]"]]]], "+", RowBox[List["30", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", RowBox[List["ModularLambda", "[", "z", "]"]]]]]], ")"]]]], "-", RowBox[List["10", RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "3"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["ModularLambda", "[", "z", "]"]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "2"]]]]], ")"]]]], "+", " ", RowBox[List[SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["4", " ", RowBox[List["ModularLambda", "[", "z", "]"]]]], "+", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "2"], "+", RowBox[List["6", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "3"]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "4"]]]]], ")"]]]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mn> 5 </mn> </msup> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 512 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mtext> </mtext> </mrow> <msup> <mi> π </mi> <mn> 5 </mn> </msup> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msup> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <msup> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <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]], ")"]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 5 </cn> </degree> </bvar> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 512 </cn> <imaginaryi /> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <ci> EllipticK </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "5"]], "}"]]]]], RowBox[List["ModularLambda", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["512", " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "6"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["ModularLambda", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "4"]]], "-", RowBox[List["60", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "3"], " ", RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], " ", RowBox[List["ModularLambda", "[", "z", "]"]]]], "+", RowBox[List["30", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", RowBox[List["ModularLambda", "[", "z", "]"]]]]]], ")"]]]], "-", RowBox[List["10", " ", RowBox[List["EllipticE", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "3"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["ModularLambda", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["ModularLambda", "[", "z", "]"]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["ModularLambda", "[", "z", "]"]], "]"]], "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["4", " ", RowBox[List["ModularLambda", "[", "z", "]"]]]], "+", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "2"], "+", RowBox[List["6", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "3"]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["ModularLambda", "[", "z", "]"]], "4"]]]]], ")"]]]]]], ")"]]]], SuperscriptBox["\[Pi]", "5"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
