Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers. (English) Zbl 1537.11037
This paper’s content covers the Bell polynomial of the second kind, the Boole number, the Boole polynomial, determinantal expression, generating function, the Hessenberg determinant, the Peters number, the Peters polynomial, recursive relation. This content has very important applications in combinatorics, probability theory, and in applied sciences. By applying the Faà di Bruno formula with the Bell polynomials of the second kind, the author gives many formulas for the Peters polynomials and numbers and also derivative formulas. The author also gives recursive relations for the Peters polynomials and numbers. Moreover, he gives some applications for alternative recursive relations and recursive relation for the Hessenberg determinants involving these numbers an polynomials and also the Boole polynomials and numbers.
Reviewer: Yilmaz Simsek (Antalya)
MSC:
| 11B83 | Special sequences and polynomials |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 11B37 | Recurrences |
| 11C20 | Matrices, determinants in number theory |
| 11Y55 | Calculation of integer sequences |
| 33B15 | Gamma, beta and polygamma functions |
Keywords:
Bell polynomial of the second kind; Boole number; Boole polynomial; determinantal expression; explicit formula; generating function; Hessenberg determinant; Peters number; Peters polynomial; recursive relationReferences:
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