Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions

In the paper, the authors 1. establish general expressions of series expansions of [(arcsin x).sup.l] for l [member of] N; 2. find closed-form formulas for the sequence [Please download the PDF to view the mathematical expression], where [B.sub.n,k] denotes the second kind Bell polynomials; 3. deriv...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:AIMS Mathematics 2021-01, Vol.6 (7), p.7494-7517
Hauptverfasser: Guo, Bai-Ni, Lim, Dongkyu, Qi, Feng
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In the paper, the authors 1. establish general expressions of series expansions of [(arcsin x).sup.l] for l [member of] N; 2. find closed-form formulas for the sequence [Please download the PDF to view the mathematical expression], where [B.sub.n,k] denotes the second kind Bell polynomials; 3. derive series representations of generalized logsine functions. The series expansions of the powers [(arcsin x).sup.l] were related with series representations for generalized logsine functions by Andrei I. Davydychev, Mikhail Yu. Kalmykov, and Alexey Sheplyakov. The above sequence represented by special values of the second kind Bell polynomials appeared in the study of Grothendieck's inequality and completely correlation-preserving functions by Frank Oertel. Keywords: general expression; closed-form formula; arcsine; series expansion; power; special value; second kind Bell polynomials; series representation; generalized logsine function
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021438