A study on \(\lambda\)-Sheffer sequences by other \(\lambda\)-Sheffer sequences. (English) Zbl 1498.05039
Summary: Recently, \(\lambda\)-umbral calculus has been developed in order to study degenerate Sheffer polynomials and \(\lambda\)-Sheffer polynomials, starting from the simple question that what if we replace the usual exponential function by the degenerate exponential function in the generating function of Sheffer polynomials. The aim of this paper is to represent some \(\lambda\)-Sheffer polynomials by other \(\lambda\)-Sheffer polynomials. These are done by using some formulas derived from the definition of existence of \(\lambda\)-Sheffer polynomials.
MSC:
05A40 | Umbral calculus |
11B68 | Bernoulli and Euler numbers and polynomials |
11B73 | Bell and Stirling numbers |
11B83 | Special sequences and polynomials |