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:

    Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.
    Walter Pater (1839–1894)

    Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.
    The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)

    I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)