{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:44:42Z","timestamp":1760402682050,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T00:00:00Z","timestamp":1617321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of fractional degree, and we show possible applications of these new functions. For the first kind, we compute the fractional Newton sum rules of any orthogonal polynomial set starting from the entries of the Jacobi matrix. For the second kind, the representation formulas for the fractional powers of a r\u00d7r matrix, already introduced by using the pseudo-Chebyshev functions, are extended to the Lucas case.<\/jats:p>","DOI":"10.3390\/axioms10020051","type":"journal-article","created":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T10:34:09Z","timestamp":1617359649000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Pseudo-Lucas Functions of Fractional Degree and Applications"],"prefix":"10.3390","volume":"10","author":[{"given":"Clemente","family":"Cesarano","sequence":"first","affiliation":[{"name":"Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierpaolo","family":"Natalini","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo, 1, 00146 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7899-3087","authenticated-orcid":false,"given":"Paolo","family":"Ricci","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1029\/2018RS006750","article-title":"Incomplete Anger-Weber Functions: A Class of Special Functions for Electromagnetics","volume":"54","author":"Caratelli","year":"2019","journal-title":"Radio Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0096-3003(02)00328-4","article-title":"On a new family of Hermite polynomials associated to parabolic cylinder functions","volume":"141","author":"Dattoli","year":"2003","journal-title":"Appl. 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