SiftedEtaQuotientGamma(C, mx, CX, xi, LX)ΒΆ
- C: Join(Algebra Fraction Integer , IntegralDomain )
- mx: PositiveInteger
- CX: Algebra C
- xi: CX
- LX: UnivariateLaurentSeriesCategory CX
SiftedEtaQuotientGamma is a generalization of EtaQuotientGamma. It holds data to compute an eta quotient expansion of $g_
{s
,m
,t
,lambda}(gamma tau)$, $g_
{s
,m
,t
}(gamma tau)$, $F_
{r
,s
,m
,t
}(gamma tau)$. See eqref{eq:g_s-m
-t
-lambda(gamma*tau)}.}
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- expansion: % -> LX
expansion(x)
returns the Laurent series representation ofx
without the prefactor corresponding to $(c
tau +d
)$ in z=q^(1/d) where d=rationalPowerDenominator(x
).
- puiseux: (SymbolicModularSiftedEtaQuotientGamma, PositiveInteger ) -> %
puiseux(y, w)
represents theq
-expansion of $F_
{r
,s
,m
,t
}(gamma tau)$ at $tau=i infity$.
- puiseux: (SymbolicSiftedEtaQuotientGamma, PositiveInteger ) -> %
puiseux(y, w)
represents theq
-expansion of $g_
{s
,m
,t
}(gamma tau)$ at $tau=i infity$.
- puiseux: (SymbolicSiftedEtaQuotientLambdaGamma, PositiveInteger ) -> %
puiseux(y, w)
represents theq
-expansion ofg_
{s
,m
,t
,lambda}(gamma tau) at tau=i infity.
- puiseux: (SymbolicSiftedEtaQuotientOrbitProductGamma, PositiveInteger ) -> %
puiseux(y, w)
represents theq
-expansion of $prod_{t'
in modularOrbit{s
,m
,t
}}g_
{s
,m
,t
}(gamma tau)$ at $tau=i infity$.
- rationalPowerDenominator: % -> PositiveInteger
rationalPowerDenominator(x)
returnsd
such thatx
is a Laurent series inq^d
.