Definition
In general, the orthogonal polynomials Pn with respect to a weight W:R→R+ on the real line are defined by
The relations above define Pn up to multiplication by a number. Various normalisations are used to fix the constant, e.g.
The classical orthogonal polynomials correspond to the three families of weights:
The standard normalisation (also called standardization) is detailed below.
Read more about this topic: Classical Orthogonal Polynomials
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 (18391894)
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth mans fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)