Some Orthogonal q-Polynomials
β Scribed by W. A. Al-Salam; L. Carlitz
- Publisher
- John Wiley and Sons
- Year
- 1965
- Tongue
- English
- Weight
- 413 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
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.
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
Starting from the Delsarte Genin (DG) mapping of the symmetric orthogonal polynomials on an interval (OPI) we construct a one-parameter family of polynomials orthogonal on the unit circle (OPC). The value of the parameter defines the arc on the circle where the weight function vanishes. Some explici