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type/SERIES

SERIES data structure

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

type(expr, SERIES)

Parameters

expr

-

algebraic expression

Description

• 

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:

1. 

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

2. 

the list of coefficients, which can be SERIES themselves;

3. 

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);

4. 

the common type of its coefficients;

5. 

the list of exponents;

6. 

the exponent of the O... term;

7. 

the type of the exponents;

8. 

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

9. 

the expression being expanded.

Examples

with(MultiSeries,multiseries):

s := multiseries(sin(x),x,3);

sxx36+Ox4

(1)

lprint(s);

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

s := multiseries(1/x+5+6*x^2,x,3);

s1x+5+6x2

(2)

lprint(s);

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

f := 1/(1-exp(-1/x)/(1-x))-1;

f11ⅇ1x1x1

(3)

s := multiseries(f,x,1):

s := multiseries(f,op(1,s),3,op(1,s)[list][2..2]);

s11xⅇ1x+11x2ⅇ1x2+O1ⅇ1x3

(4)

lprint(s);

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])))

See Also

MultiSeries

MultiSeries[multiseries]

type[series]