On λ-linear functionals arising from p-adic integrals on Zp

The aim of this paper is to determine the λ -linear functionals sending any given polynomial p ( x ) with coefficients in C p to the p -adic invariant integral of P ( x ) on Z p and also to that of P ( x 1 + ⋯ + x r ) on Z p r . We show that the former is given by the generating function of degenera...

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Bibliographic Details
Published in:Advances in difference equations 2021-12, Vol.2021 (1)
Main Authors: Kim, Dae San, Kim, Taekyun, Kwon, Jongkyum, Lee, Si-Hyeon, Park, Seongho
Format: Article
Language:English
Subjects:
Algebra
Analysis
Calculus
Difference and Functional Equations
Difference Equations
Functional Analysis
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Special Functions and Orthogonal Polynomials
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Summary:The aim of this paper is to determine the λ -linear functionals sending any given polynomial p ( x ) with coefficients in C p to the p -adic invariant integral of P ( x ) on Z p and also to that of P ( x 1 + ⋯ + x r ) on Z p r . We show that the former is given by the generating function of degenerate Bernoulli polynomials and the latter by that of degenerate Bernoulli polynomials of order r . For this purpose, we use the λ -umbral algebra which has been recently introduced by Kim and Kim (J. Math. Anal. Appl. 493(1):124521 2021 ).
ISSN:1687-1839
1687-1847
DOI:10.1186/s13662-021-03634-z