Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions

Kilar N., ŞİMŞEK Y., Srivastava H. M.

RAMANUJAN JOURNAL, cilt.61, sa.3, ss.731-756, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s11139-022-00679-w
  • Dergi Adı: RAMANUJAN JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.731-756
  • Akdeniz Üniversitesi Adresli: Evet

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.