The Indefinite(f, k) command computes a closed form of the indefinite sum of  with respect to .

The command uses a combination of algorithms handling various classes of summands. They include the classes of polynomials, rational functions, and hypergeometric terms and j-fold hypergeometric terms, functions for which their minimal annihilators can be constructed, for example, d'Alembertian terms. For more information, see LinearOperators.

A library extension mechanism is also used to include sums for which an algorithmic approach to finding closed forms does not yet exist. Currently the computable summands include expressions containing the harmonic function, logarithmic function, digamma and polygamma functions, and sin, cos, and the exponential functions.

If the option failpoints=true (or just failpoints for short) is specified, then the command returns a pair , where

 is a closed form of the indefinite sum of  w.r.t. , as above,

 is a list of intervals  where  does not exist, and

 is a list of points  where the computed sum  does not satisfy the telescoping equation  or does not exist.

If such points appear in the summation interval, the discrete Newton-Leibniz formula may fail.

If the command is unable to compute one of the lists , the command returns .

Error, numeric exception: division by zero

Error, numeric exception: division by zero