# StreamExponentialSeriesOperations CoefΒΆ

- Coef: CommutativeRing

StreamExponentialSeriesOperations implements arithmetic of exponential power series, where a power series is represented by a stream of its coefficients.

- *: (Stream Coef, Stream Coef) -> Stream Coef
`a * b`

returns the power series (Cauchy) product of`a`

and`b:`

`[a0, a1, ...] * [b0, b1, ...] = [c0, c1, ...]`

where`ck = sum(i + j = k, binomial(k, i) * ai * bj)`

.

- deriv: Stream Coef -> Stream Coef
`deriv(f)`

is the derivative, which simply coincides with left shift

- exp0: Stream Coef -> Stream Coef
`exp0(f)`

returns the exponential of the power series represented by cons(0,`f`

), i.e. assuming zero constant term and therefore transcendentality is not involved.

- integrate: (Coef, Stream Coef) -> Stream Coef
`integrate(c, f)`

integrates with constant term`c`

, this is simply the right shift