It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing ortho
Orthogonal Homogeneous Polynomials
β Scribed by A. Fryant; A. Naftalevich; M.K. Vemuri
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 71 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0196-8858
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β¦ Synopsis
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.
π SIMILAR VOLUMES
In this paper, we study orthogonal polynomials with respect to the inner product Ε½ . Ε½N. Β² : , where G 0 for m s 1, . . . , N, and u is a semiclassical, positive definite linear functional. For these non-standard orthogonal polynomials, algebraic and differential properties are obtained, as well a
Let the orthogonal multiplicity of a monic polynomial g over a field % be the number of polynomials f over %, coprime to g and of degree less than that of g, such that all the partial quotients of the continued fraction expansion of f/g are of degree 1. Polynomials with positive orthogonal multiplic
Stein's method provides a way of finding approximations to the distribution, say, of a random variable, which at the same time gives estimates of the approximation error involved. In essence the method is based on a defining equation, or equivalently an operator, of the distribution and a related St