The function type/SERIES returns true if the value of expr is Maple's SERIES data structure, explained below.

The SERIES data structure represents an expression as a truncated series in one specified indeterminate, expanded at a particular point. A call to the MultiSeries[multiseries] function will always return an object of this type, or 0.

The SERIES structure has nine entries:

the scale (a table, see MultiSeries,scale);

the list of coefficients, which can be SERIES themselves;

the coefficient of the $\mathrm{O}\left(...\right)$ term, which can be a function of the variable varying more slowly than the expansion variable. It is 0 if the series is exact with respect to its expansion variable (see below);

the common type of its coefficients;

the list of exponents;

the exponent of the $\mathrm{O}\left(...\right)$ term;

the type of the exponents;

the expansion variable, i.e. the element of the asymptotic basis being used;

the expression being expanded.

$\mathrm{with}\left(\mathrm{MultiSeries}\,\mathrm{multiseries}\right)\:$

$s≔\mathrm{multiseries}\left(\sin \left(x\right)\,x\,3\right)$

$s≔x-\frac{x^3}{6}+\mathrm{O}\left(x^4\right)$

$\mathrm{lprint}\left(s\right)$

SERIES(Scale,[1, -1/6],1,rational,[1, 3],4,integer,_var[x],sin(_var[x]))

$s≔\mathrm{multiseries}\left(\frac{1}{x}+5+6x^2\,x\,3\right)$

$s≔\frac{1}{x}+5+6x^2$

$\mathrm{lprint}\left(s\right)$

SERIES(Scale,[1, 5, 6],0,integer,[-1, 0, 2],infinity,integer,_var[x],1/_var[x]+5+6*_var[x]^2)

$f≔\frac{1}{1-\frac{\exp \left(-\frac{1}{x}\right)}{1-x}}-1$

$f≔\frac{1}{1-\frac{{\ⅇ}^{-\frac{1}{x}}}{1-x}}-1$

$s≔\mathrm{multiseries}\left(f\,x\,1\right)\:$

$s≔\mathrm{multiseries}\left(f\,\mathrm{op}\left(1\,s\right)\,3\,\mathrm{op}\left(1\,s\right)\left[\mathrm{list}\right]\left[2..2\right]\right)$

$s≔\frac{1}{\left(1-x\right){\ⅇ}^{\frac{1}{x}}}+\frac{1}{{\left(1-x\right)}^2{\left({\ⅇ}^{\frac{1}{x}}\right)}^2}+\mathrm{O}\left(\frac{1}{{\left({\ⅇ}^{\frac{1}{x}}\right)}^3}\right)$

$\mathrm{lprint}\left(s\right)$

SERIES(Scale,[1/(1-_var[x]), 1/(1-_var[x])^2],1,algebraic,[1, 2],3,integer,_var[1/exp(1/x)],-1+1/(1-_var[1/exp(1/x)]/(1-_var[x])))