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 thateqi
is 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 byrspec
, with parameters (m
,t
) and multiplied by the etaquotient given bysspec
. It corresponds toF_
{s
,r
,m
,t
}(tau) as given through Equation eqref{eq:Ramanuja-Kolberg-Identity}.
- laurentExpansionInfinity: QEtaSpecification -> QEtaLaurentSeries C
laurentExpansionInfinity(spec)
computes the $q
$-series Laurent expansion of the eta-quotient given byspec
.
- modularEtaQuotientInfinity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> ModularFunctionQSeriesInfinity C if C has CommutativeRing
modularEtaQuotientInfinity(sspec, rspec, m, t)
returns the series expansion of etaQuotient(sspec
,rspec
,m
,t
)$SymbolicModularEtaQuotientGamma(QMOD) at the cusp infinity without using SymbolicModularEtaQuotientGamma.
- modularEtaQuotientInfinity: QEtaSpecification -> ModularFunctionQSeriesInfinity C if C has CommutativeRing
modularEtaQuotientInfinity(rspec)
checks whetherrspec
specifices modular eta-quotientwrt
. QMOD and returns (expansion(etaQuotient(rspec
)$EQI(C
))$EQI(C
))::A1
(C
).