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A Class of Orthogonal Polynomials on the Radial Rays in the Complex Plane

✍ Scribed by Gradimir V Milovanović

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
202 KB
Volume
206
Category
Article
ISSN
0022-247X

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✦ Synopsis

We introduce a class of polynomials orthogonal on some radial rays in the complex plane and investigate their existence and uniqueness. A recurrence relation for these polynomials, a representation, and the connection with standard Ž . polynomials orthogonal on 0, 1 are derived. It is shown that their zeros are simple and distributed symmetrically on the radial rays, with the possible exception of a multiple zero at the origin. An analogue of the Jacobi polynomials and the corresponding problem with the generalized Laguerre polynomials are also treated.

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