Companion orthogonal polynomials
β Scribed by A. Sri Ranga
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 377 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
β¦ Synopsis
We give some properties relating the recurrence relations of orthogonal polynomials associated with any two symmetric distributions d~bl(x) and d~b2(x) such that dq~2(x) = (1 + kx2)dq~l(x). As applications of these properties, recurrence relations for many interesting systems of orthogonal polynomials are obtained.
π SIMILAR VOLUMES
An addition formula, Pythagorean identity, and generating function are obtained for orthogonal homogeneous polynomials of several real variables. Application is made to the study of series of such polynomials. Results include an analog of the Funk-Hecke theorem.
The Galerkin method offers a powerful tool in the solution of differential equations and function approximation on the real interval [Γ1, 1]. By expanding the unknown function in appropriately chosen global basis functions, each of which explicitly satisfies the given boundary conditions, in general