| Title | On the Relation Between Gegenbauer Polynomials and the Ferrers Function of the First Kind |
|---|---|
| Authors | Cohl, H. S. , COSTAS SANTOS, ROBERTO SANTIAGO |
| External publication | Si |
| Means | Anal. Math. |
| Scope | Article |
| Nature | Científica |
| JCR Quartile | 3 |
| SJR Quartile | 2 |
| JCR Impact | 0.7 |
| SJR Impact | 0.521 |
| Web | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85127428489&doi=10.1007%2fs10476-022-0123-0&partnerID=40&md5=5418f3aa6373f1b4fbe666de96766cc6 |
| Publication date | 01/09/2022 |
| ISI | 000775954200003 |
| Scopus Id | 2-s2.0-85127428489 |
| DOI | 10.1007/s10476-022-0123-0 |
| Abstract | Using the direct relation between the Gegenbauer polynomials Cn(lambda)(x) and the Ferrers function of the first kind P nu(mu)(x), we compute interrelations between certain Jacobi polynomials, Meixner polynomials, and Ferrers functions of the first and second kind. We then compute Rodrigues-type, standard integral orthogonality and Sobolev orthogonality relations for Ferrers functions of the first and second kinds. In the remainder of the paper using the relation between Gegenbauer polynomials and the Ferrers function of the first kind we derive connection and linearization relations, some definite integral and series expansions, Christoffel-Darboux summation formulas, Poisson kernel and infinite series closure relations (Dirac delta distribution expansions). |
| Keywords | Ferrers function; Gegenbauer polynomial; orthogonal polynomial; orthogonality relation; Christoffel-Darboux summation; Poisson kernel; closure relation |
| Universidad Loyola members |