R> Actually the example makes it necessary to completely abandon
R> the original GiNaC series code and use Maxima as fallback in the
R> cases that cannot be handled by the fast rational Pynac series code.
Unfortunately this will not help much. Maxima/taylor is also
unable to compute these functions even for modest values of m
efficiently as you can see from the next example:
def P(m, n):
x, z = var('x, z')
if m == 1: return Integer(1)
w = exp(2 * pi * I / m)
o = sum(exp(z * w^k) for k in range(m)) / m
f = exp(z*x) * (exp(z) / o - 1)
t = f.taylor(z, 0, n+1)
return factorial(n) * t.coefficient(z, n)
for m in [1,2,3,4,5,6,7,11,13]:
print [m], [P(m, n).subs(x=0) for n in (0..10)]
AFAIK there is only one CAS which can handle these things
(which are basic!) efficiently: Mathematica. So if I would
put something on trac it would be an enhancement request:
"Implement the Mittag-Leffler function!".
Peter
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