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.
Orthogonal Newton polynomials
β Scribed by Louis de Branges; David Trutt
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 902 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
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