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Approximate Sums Numerically

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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);

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)

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