In order to find recurrence relation, numerical values, and other useful properties of the coefficients we use the method of generating functions. Such we call the function which has the as coefficients in its Maclaurin expansion. Using the general form of the binomial theorem, we find

=

The integral is easily evaluated by writing . We thus find

(7.5)

which can be written as

,

Using the well-known expansions

(7.6)