Orthogonal Polynomial
An Orthogonal Polynomial is a polynomial that ...
- Example(s):
- See: Orthogonality, Inner Product, Classical Orthogonal Polynomials, Hermite Polynomials, Laguerre Polynomials, Jacobi Polynomials, Gegenbauer Polynomials, Chebyshev Polynomials, Legendre Polynomials.
References
2016
- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/orthogonal_polynomials Retrieved:2016-10-23.
- In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the Gegenbauer polynomials, the Chebyshev polynomials, and the Legendre polynomials.
The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes. Some of the mathematicians who have worked on orthogonal polynomials include Gábor Szegő, Sergei Bernstein, Naum Akhiezer, Arthur Erdélyi, Yakov Geronimus, Wolfgang Hahn, Theodore Seio Chihara, Mourad Ismail, Waleed Al-Salam, and Richard Askey.
- In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.