If the sum command cannot compute a sum, MuPAD® returns an unresolved sum. For example, try to compute the following sum:
sum(exp(x)^(-x), x = 0..infinity)
The reasons MuPAD cannot compute the closed form of a particular sum are the same as the reasons for not computing an integral:
The antidifference does not exist in a closed form.
The antidifference exists, but MuPAD cannot find it.
MuPAD can find the antidifference on a larger computer, but runs out of time or memory on the available machine.
If MuPAD cannot compute a definite sum, try to approximate it numerically:
S := sum(exp(x)^(-x), x = 0..infinity); float(S)
If you know in advance that the antidifference cannot be computed in a closed form, skip trying to calculate this sum symbolically. For such expressions, call the numeric::sum function to perform numeric summation directly. Trying to calculate a symbolic sum, and then approximating it numerically can be much slower than applying numeric summation from the beginning:
numeric::sum(exp(x)^(-x), x = 0..infinity)