Representation of Formal Power Series
Description
Examples
Formal power series are procedures that return the coefficients of the power series they represent. Thus namei is the coefficient of xi in the series called name.
The values of the coefficients are saved using a remember table, so all computed coefficients can be seen via op(4, op(name)).
The actual procedure is identical for all power series; the only differences are the general term and the values that each remembers.
The general term of the power series can be obtained via name(_k) .
Note that each intermediate power series created in a calculation should be named.
withpowseries:
powcreateen=1n!,e0=1:
powcreatefn=fn−1n2fn−2,f0=1,f1=5,f2=2:
tpsforme,x,6
1+x+12x2+16x3+124x4+1120x5+Ox6
tpsformf,x,6
1+5x+2x2+245x3+1720x4+1800x5+Ox6
Compute the series f^e .
logf≔powlogf:
elogf≔multiplye,logf:
result≔powexpelogf:
tpsformresult,x,6
1+5x+7x2+76745x3+2351240x4+39231800x5+Ox6
See Also
powseries
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