Q-difference Polynomial - Definition

Definition

The q-difference polynomials satisfy the relation

\left(\frac {d}{dz}\right)_q p_n(z) =
\frac{p_n(qz)-p_n(z)} {qz-z} = p_{n-1}(z)

where the derivative symbol on the left is the q-derivative. In the limit of, this becomes the definition of the Appell polynomials:

Read more about this topic:  Q-difference Polynomial

Famous quotes containing the word definition:

    Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?
    Richard Eberhart (b. 1904)

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.
    François, Duc De La Rochefoucauld (1613–1680)