ModularEtaQuotientQSeriesInfinityTools(C, QMOD)ΒΆ
qetamodeqqseriesinftool.spad line 76 [edit on github]
- C: Ring 
- QMOD: QEtaModularCategory 
undocumented
- coerce: EtaQuotientQSeriesInfinity C -> ModularFunctionQSeriesInfinity C if C has CommutativeRing
- coerce(x)assumes that eqi is the representation of a modular eta-quotient with a cusp only at infinity and expands it into a Laurent series.
- coerce: EtaQuotientQSeriesInfinity C -> QEtaLaurentSeries C
- coerce(eqi)assumes that- eqiis the representation of an eta-quotient and expands it into a Laurent series.
- laurentExpansionInfinity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> QEtaLaurentSeries C
- laurentExpansionInfinity(sspec,rspec,m,t)computes the $- q$-series Laurent expansion corresponding to the disection of the eta-quotient given by- rspec, with parameters (- m,- t) and multiplied by the etaquotient given by- sspec. It corresponds to- F_{- s,- r,- m,- t}(tau) as given through Equation eqref{eq:Ramanuja-Kolberg-Identity}.
- laurentExpansionInfinity: QEtaSpecification -> QEtaLaurentSeries C
- laurentExpansionInfinity(spec)computes the $- q$-series Laurent expansion of the eta-quotient given by- spec.
- modularEtaQuotientInfinity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> ModularFunctionQSeriesInfinity C if C has CommutativeRing
- modularEtaQuotientInfinity(sspec, rspec, m, t)returns the series expansion of etaQuotient(- sspec,- rspec,- m,- t)$SymbolicModularEtaQuotientGamma(QMOD) at the cusp infinity without using SymbolicModularEtaQuotientGamma.
- modularEtaQuotientInfinity: QEtaSpecification -> ModularFunctionQSeriesInfinity C if C has CommutativeRing
- modularEtaQuotientInfinity(rspec)checks whether- rspecspecifices modular eta-quotient- wrt. QMOD and returns (expansion(etaQuotient(- rspec)$EQI(- C))$EQI(- C))- ::A1(- C).