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 0.70000
SJR Impact 0.52100
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
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