SiftedEtaQuotientGamma(C, mx, CX, xi, LX)

qetafun.spad line 3200

• 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 of x without the prefactor corresponding to $(c tau + d)$ in z=q^(1/d) where d=rationalPowerDenominator(x).

puiseux: (SymbolicModularSiftedEtaQuotientGamma, PositiveInteger ) -> %

puiseux(y, w) represents the q-expansion of $F_{r,s,m,t}(gamma tau)$ at $tau=i infity$.

puiseux: (SymbolicSiftedEtaQuotientGamma, PositiveInteger ) -> %

puiseux(y, w) represents the q-expansion of $g_{s,m,t}(gamma tau)$ at $tau=i infity$.

puiseux: (SymbolicSiftedEtaQuotientLambdaGamma, PositiveInteger ) -> %

puiseux(y, w) represents the q-expansion of g_{s,m,t,lambda}(gamma tau) at tau=i infity.

puiseux: (SymbolicSiftedEtaQuotientOrbitProductGamma, PositiveInteger ) -> %

puiseux(y, w) represents the q-expansion of $prod_{t' in modularOrbit{s,m,t}} g_{s,m,t}(gamma tau)$ at $tau=i infity$.

rationalPowerDenominator: % -> PositiveInteger

rationalPowerDenominator(x) returns d such that x is a Laurent series in q^d.

CoercibleTo OutputForm