Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions
Küçük Resim Yok
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The aim of this paper is to obtain some interesting infinite series representations for the Apostol-type parametrically generalized polynomials with the aid of the Laplace transform and generating functions. In particular, by using the method of generating functions, we derive not only recurrence relations, but also several other formulas, identities, and relations as well as combinatorial sums for these parametrically generalized numbers and polynomials and for other known special numbers and polynomials. These identities, relations and combinatorial sums are related to the two-parameter types of the Apostol-Bernoulli polynomials of higher order, the two-parameter types of Apostol-Euler polynomials of higher order, the two-parameter types of Apostol-Genocchi polynomials of higher order, the Apostol-Bernoulli polynomials of higher order, the Apostol-Euler polynomials of higher order, the Apostol-Genocchi polynomials of higher order, the cosine- and sine-Bernoulli polynomials, the cosine- and sine-Euler polynomials, the lambda-array-type polynomials, the lambda-Stirling numbers, the polynomials C-n(x,y)Cn(x,y), and the polynomials S-n(x,y)Sn(x,y). Finally, we present several new recurrence relations for these special polynomials and numbers.
Açıklama
Anahtar Kelimeler
Apostol-Bernoulli numbers and polynomials, Apostol-Euler numbers and polynomials, Apostol-Genocchi numbers and polynomials, Parametrically generalized numbers and polynomials, Special numbers and polynomials, Laplace transform, Generating functions
Kaynak
Ramanujan Journal
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
61
Sayı
3
