__Introduction to the Mgfun Package__

The
**Mgfun**
package consists of procedures to compute with special functions and combinatorial sequences that are implicitly defined as solutions of systems of linear difference-differential equations. Its syntax is very close to that of the
**gfun**
package. In the same spirit as with the latter, a typical use of
**Mgfun**
to compute a sum or integral is the following. First one obtains systems that define the summand or integrand by calls to
__dfinite_expr_to_sys__
or by combining known systems by using
__`sys+sys`__
and
__`sys*sys`__
. Then one derives the sum or integral by a call to
__sum_of_sys__
or
__int_of_sys__
. Finally one has to solve the system to obtain a closed form (if one exists).

`> `
**with(Mgfun);**

In the sequel, we exemplify the use of the package by working out the evaluation of a sum and of two integrals.

**Closed Form Evaluation of **

**Closed Form Evaluation of **

**Chebyshev Coefficients of **