| Título |
On the Relation Between Gegenbauer Polynomials and the Ferrers Function of the First Kind |
| Autores |
Cohl, H. S. , COSTAS SANTOS, ROBERTO SANTIAGO |
| Publicación externa |
Si |
| Medio |
Analysis Mathematica |
| Alcance |
Article |
| Naturaleza |
Científica |
| Cuartil JCR |
3 |
| Cuartil SJR |
2 |
| Impacto JCR |
0.7 |
| Impacto SJR |
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 |
| Fecha de publicacion |
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). |
| Palabras clave |
Ferrers function; Gegenbauer polynomial; orthogonal polynomial; orthogonality relation; Christoffel-Darboux summation; Poisson kernel; closure relation |
| Miembros de la Universidad Loyola |
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