Q-difference Polynomial - Generating Function

Generating Function

The generating function for these polynomials is of the type of generating function for Brenke polynomials, namely

where is the q-exponential:

e_q(t)=\sum_{n=0}^\infty \frac{t^n}{_q!}= \sum_{n=0}^\infty \frac{t^n (1-q)^n}{(q;q)_n}.

Here, is the q-factorial and

is the q-Pochhammer symbol. The function is arbitrary but assumed to have an expansion

Any such gives a sequence of q-difference polynomials.

Read more about this topic:  Q-difference Polynomial

Famous quotes containing the word function:

    “Think of the tools in a tool-box: there is a hammer, pliers, a saw, a screwdriver, a rule, a glue-pot, nails and screws.—The function of words are as diverse as the functions of these objects.”
    —Ludwig Wittgenstein (1889–1951)