Using deftaylor with an infinite sum produces fewer display terms than with
a finite sum (polynomial). While this may be a feature, I suspect I'm
missing what option controls this behavior. To illustrate, running Xmaxima
from a Maxima-5.28.0-2 distribution (same behavior observed in wxMaxima):
(%i1) deftaylor(F(x), sum(x^(k+3)*bern(k)/(k!*(k+3)), k, 0, inf));
(%o1) [F]
(%i2) taylor(F(x),x,0,15);
3 4 5
x x x
(%o2)/T/ -- - -- + -- + . . .
3 8 60
(%i3) deftaylor(F(x), sum(x^(k+3)*bern(k)/(k!*(k+3)), k, 0, 30));
deftaylor: redefining F.
(%o3) [F]
(%i4) taylor(F(x),x,0,15);
3 4 5 7 9 11 13
x x x x x x x
(%o4)/T/ -- - -- + -- - ---- + ------ - -------- + ---------
3 8 60 5040 272160 13305600 622702080
15
691 x
- -------------- + . . .
19615115520000
(%i5) maxtayorder;
(%o5) true
(%i6) zerobern;
(%o6) true
Notice that for the infinite sum, taylor displays only three terms, less
than the requested length of expansion, but for the finite sum the full
requested length is provided.
I suspect this may hinge on hitting the first "missing" coefficient
in the infinite sum, i.e. x^6 has zero coefficient from bernoulli
numbers. The documentation of function pade hints that "truncation
level" and "order of series" are properties of a power series, but
otherwise the documentation does not explain how these are set or
inferred.
regards, chip