Orthogonal Polynomials with Ultra-Exponential Weight Functions: An Explicit Solution to the Ditkin-Prudnikov Problem

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Yakubovich, SB (Author) FCUP

Journal

Title: Constructive Approximation

Vol. 53

Pages: 1-38

ISSN: 0176-4276

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 4 Citations

Scopus - 4 Citations

Other information

Authenticus ID: P-00T-9D4

DOI: 10.1007/s00365-020-09523-0

Abstract (EN): New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, we give an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are derived. The method is based on differential properties of the involved special functions and their representations in terms of the Mellin-Barnes and Laplace integrals. A notion of the composition polynomial orthogonality is introduced. The corresponding advantages of this orthogonality to discover new sequences of polynomials and their relations to the corresponding multiple orthogonal polynomial ensembles are shown.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 38