SERIES data structure
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 O⁡... 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 O⁡... term;
the type of the exponents;
the expansion variable, i.e. the element of the asymptotic basis being used;
the expression being expanded.
s ≔ multiseries⁡sin⁡x,x,3
SERIES(Scale,[1, -1/6],1,rational,[1, 3],4,integer,_var[x],sin(_var[x]))
s ≔ multiseries⁡1x+5+6⁢x2,x,3
SERIES(Scale,[1, 5, 6],0,integer,[-1, 0, 2],infinity,integer,_var[x],1/_var[x]+5+6*_var[x]^2)
f ≔ 11−ⅇ−1x1−x−1
s ≔ multiseries⁡f,x,1:
s ≔ multiseries⁡f,op⁡1,s,3,op⁡1,slist2..2
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])))
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