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)

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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> <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> 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</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 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2001-10-29