Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











EllipticNomeQ






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticNomeQ[m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/09.53.06.0001.01









  


  










Input Form





EllipticNomeQ[m] \[Proportional] m/16 + m^2/32 + (21 m^3)/1024 + (31 m^4)/2048 + (6257 m^5)/524288 + (10293 m^6)/1048576 + (279025 m^7)/33554432 + (483127 m^8)/67108864 + (435506703 m^9)/68719476736 + (776957575 m^10)/137438953472 + (22417045555 m^11)/4398046511104 + (40784671953 m^12)/8796093022208 + (9569130097211 m^13)/2251799813685248 + (17652604545791 m^14)/ 4503599627370496 + (523910972020563 m^15)/144115188075855872 + (976501268709949 m^16)/288230376151711744 + (935823746406530603 m^17)/ 295147905179352825856 + (1758220447807291611 m^18)/ 590295810358705651712 + (53030538453624441751 m^19)/ 18889465931478580854784 + (100268465197007602645 m^20)/ 37778931862957161709568 + O[m^21] /; (m -> 0)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticNomeQ", "[", "m", "]"]], "\[Proportional]", RowBox[List[FractionBox["m", "16"], "+", FractionBox[SuperscriptBox["m", "2"], "32"], "+", FractionBox[RowBox[List["21", " ", SuperscriptBox["m", "3"]]], "1024"], "+", FractionBox[RowBox[List["31", " ", SuperscriptBox["m", "4"]]], "2048"], "+", FractionBox[RowBox[List["6257", " ", SuperscriptBox["m", "5"]]], "524288"], "+", FractionBox[RowBox[List["10293", " ", SuperscriptBox["m", "6"]]], "1048576"], "+", FractionBox[RowBox[List["279025", " ", SuperscriptBox["m", "7"]]], "33554432"], "+", FractionBox[RowBox[List["483127", " ", SuperscriptBox["m", "8"]]], "67108864"], "+", FractionBox[RowBox[List["435506703", " ", SuperscriptBox["m", "9"]]], "68719476736"], "+", FractionBox[RowBox[List["776957575", " ", SuperscriptBox["m", "10"]]], "137438953472"], "+", FractionBox[RowBox[List["22417045555", " ", SuperscriptBox["m", "11"]]], "4398046511104"], "+", FractionBox[RowBox[List["40784671953", " ", SuperscriptBox["m", "12"]]], "8796093022208"], "+", FractionBox[RowBox[List["9569130097211", " ", SuperscriptBox["m", "13"]]], "2251799813685248"], "+", FractionBox[RowBox[List["17652604545791", " ", SuperscriptBox["m", "14"]]], "4503599627370496"], "+", FractionBox[RowBox[List["523910972020563", " ", SuperscriptBox["m", "15"]]], "144115188075855872"], "+", FractionBox[RowBox[List["976501268709949", " ", SuperscriptBox["m", "16"]]], "288230376151711744"], "+", FractionBox[RowBox[List["935823746406530603", " ", SuperscriptBox["m", "17"]]], "295147905179352825856"], "+", FractionBox[RowBox[List["1758220447807291611", " ", SuperscriptBox["m", "18"]]], "590295810358705651712"], "+", FractionBox[RowBox[List["53030538453624441751", " ", SuperscriptBox["m", "19"]]], "18889465931478580854784"], "+", FractionBox[RowBox[List["100268465197007602645", " ", SuperscriptBox["m", "20"]]], "37778931862957161709568"], "+", RowBox[List["O", "[", SuperscriptBox["m", "21"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "0"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mi> m </mi> <mn> 16 </mn> </mfrac> <mo> + </mo> <mfrac> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mn> 32 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> </mrow> <mn> 1024 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 4 </mn> </msup> </mrow> <mn> 2048 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 6257 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 5 </mn> </msup> </mrow> <mn> 524288 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 10293 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 6 </mn> </msup> </mrow> <mn> 1048576 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 279025 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 7 </mn> </msup> </mrow> <mn> 33554432 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 483127 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 8 </mn> </msup> </mrow> <mn> 67108864 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 435506703 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 9 </mn> </msup> </mrow> <mn> 68719476736 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 776957575 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 10 </mn> </msup> </mrow> <mn> 137438953472 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 22417045555 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 11 </mn> </msup> </mrow> <mn> 4398046511104 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 40784671953 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 12 </mn> </msup> </mrow> <mn> 8796093022208 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 9569130097211 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 13 </mn> </msup> </mrow> <mn> 2251799813685248 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 17652604545791 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 14 </mn> </msup> </mrow> <mn> 4503599627370496 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 523910972020563 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 15 </mn> </msup> </mrow> <mn> 144115188075855872 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 976501268709949 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 16 </mn> </msup> </mrow> <mn> 288230376151711744 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 935823746406530603 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 17 </mn> </msup> </mrow> <mn> 295147905179352825856 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1758220447807291611 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 18 </mn> </msup> </mrow> <mn> 590295810358705651712 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 53030538453624441751 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 19 </mn> </msup> </mrow> <mn> 18889465931478580854784 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 100268465197007602645 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 20 </mn> </msup> </mrow> <mn> 37778931862957161709568 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> m </mi> <mn> 21 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 16 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 32 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 1024 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 2048 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6257 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <cn type='integer'> 524288 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10293 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <cn type='integer'> 1048576 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 279025 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> <apply> <power /> <cn type='integer'> 33554432 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 483127 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <cn type='integer'> 67108864 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 435506703 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 9 </cn> </apply> <apply> <power /> <cn type='integer'> 68719476736 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 776957575 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 10 </cn> </apply> <apply> <power /> <cn type='integer'> 137438953472 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22417045555 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 11 </cn> </apply> <apply> <power /> <cn type='integer'> 4398046511104 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40784671953 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 12 </cn> </apply> <apply> <power /> <cn type='integer'> 8796093022208 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9569130097211 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 13 </cn> </apply> <apply> <power /> <cn type='integer'> 2251799813685248 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17652604545791 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 14 </cn> </apply> <apply> <power /> <cn type='integer'> 4503599627370496 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 523910972020563 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 15 </cn> </apply> <apply> <power /> <cn type='integer'> 144115188075855872 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 976501268709949 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 16 </cn> </apply> <apply> <power /> <cn type='integer'> 288230376151711744 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 935823746406530603 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 17 </cn> </apply> <apply> <power /> <cn type='integer'> 295147905179352825856 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1758220447807291611 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 18 </cn> </apply> <apply> <power /> <cn type='integer'> 590295810358705651712 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 53030538453624441751 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 19 </cn> </apply> <apply> <power /> <cn type='integer'> 18889465931478580854784 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 100268465197007602645 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 20 </cn> </apply> <apply> <power /> <cn type='integer'> 37778931862957161709568 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> 21 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticNomeQ", "[", "m_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["m", "16"], "+", FractionBox[SuperscriptBox["m", "2"], "32"], "+", FractionBox[RowBox[List["21", " ", SuperscriptBox["m", "3"]]], "1024"], "+", FractionBox[RowBox[List["31", " ", SuperscriptBox["m", "4"]]], "2048"], "+", FractionBox[RowBox[List["6257", " ", SuperscriptBox["m", "5"]]], "524288"], "+", FractionBox[RowBox[List["10293", " ", SuperscriptBox["m", "6"]]], "1048576"], "+", FractionBox[RowBox[List["279025", " ", SuperscriptBox["m", "7"]]], "33554432"], "+", FractionBox[RowBox[List["483127", " ", SuperscriptBox["m", "8"]]], "67108864"], "+", FractionBox[RowBox[List["435506703", " ", SuperscriptBox["m", "9"]]], "68719476736"], "+", FractionBox[RowBox[List["776957575", " ", SuperscriptBox["m", "10"]]], "137438953472"], "+", FractionBox[RowBox[List["22417045555", " ", SuperscriptBox["m", "11"]]], "4398046511104"], "+", FractionBox[RowBox[List["40784671953", " ", SuperscriptBox["m", "12"]]], "8796093022208"], "+", FractionBox[RowBox[List["9569130097211", " ", SuperscriptBox["m", "13"]]], "2251799813685248"], "+", FractionBox[RowBox[List["17652604545791", " ", SuperscriptBox["m", "14"]]], "4503599627370496"], "+", FractionBox[RowBox[List["523910972020563", " ", SuperscriptBox["m", "15"]]], "144115188075855872"], "+", FractionBox[RowBox[List["976501268709949", " ", SuperscriptBox["m", "16"]]], "288230376151711744"], "+", FractionBox[RowBox[List["935823746406530603", " ", SuperscriptBox["m", "17"]]], "295147905179352825856"], "+", FractionBox[RowBox[List["1758220447807291611", " ", SuperscriptBox["m", "18"]]], "590295810358705651712"], "+", FractionBox[RowBox[List["53030538453624441751", " ", SuperscriptBox["m", "19"]]], "18889465931478580854784"], "+", FractionBox[RowBox[List["100268465197007602645", " ", SuperscriptBox["m", "20"]]], "37778931862957161709568"], "+", SuperscriptBox[RowBox[List["O", "[", "m", "]"]], "21"]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "0"]], ")"]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998-2014 Wolfram Research, Inc.