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answered 10 years ago

kcrisman gravatar image

Huh, this is an interesting one. In principle, it should work, but your sum is so big (not long, just complicated) that it doesn't expand.

sage: h(1)
(-e^(-33/1024*k) + 1)^k - sum(((e^(33/1024*k*x) - 1)*e^(-33/1024*k*x))^k, x, 2, 15)
sage: sum(((e^(33/1024*k*x) - 1)*e^(-33/1024*k*x))^k, x, 2, 15)
((e^(33/512*k) - 1)*e^(-33/512*k))^k + ((e^(99/1024*k) - 1)*e^(-99/1024*k))^k + ((e^(33/256*k) - 1)*e^(-33/256*k))^k + ((e^(165/1024*k) - 1)*e^(-165/1024*k))^k + ((e^(99/512*k) - 1)*e^(-99/512*k))^k + ((e^(231/1024*k) - 1)*e^(-231/1024*k))^k + ((e^(33/128*k) - 1)*e^(-33/128*k))^k + ((e^(297/1024*k) - 1)*e^(-297/1024*k))^k + ((e^(165/512*k) - 1)*e^(-165/512*k))^k + ((e^(363/1024*k) - 1)*e^(-363/1024*k))^k + ((e^(99/256*k) - 1)*e^(-99/256*k))^k + ((e^(429/1024*k) - 1)*e^(-429/1024*k))^k + ((e^(231/512*k) - 1)*e^(-231/512*k))^k + ((e^(495/1024*k) - 1)*e^(-495/1024*k))^k

This is another manifestation of this question, I think, and ultimately I think it leads to Trac 9424.

But you want a workaround, presumably. From that ticket, we can try:

plot([SR(maxima_calculus(h(l)).simplify_sum()) for l in range(1,15)], (k,10,15))

This seems to work.