Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications
By Yilmaz Simsek. 2011
164 citations recorded by the source corpus.
The first aim of this paper is to construct new generating functions for the generalized λ-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers. We derive various functional equations and differential equations using these generating functions. The second aim is to provide a novel approach to derive identities including multiplication formulas and recurrence relations for these numbers and polynomials using these functional equations and differential equations. Furthermore, we derive some new identities for the generalized λ-Stirling type numbers of the second kind, the generalized array type polynomials and the generalized Eulerian type polynomials. We also give many applications related to the class of these polynomials and numbers.MSC:12D10, 11B68, 11S40, 11S80, 26C05, 26C10, 30B40, 30C15.
Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/4938911874196a61f75ef8cdea4c63f9b5afccc5
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In Algebra and Number Theory
In Applied Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Computation methods for combinatorial sums and Euler‐type numbers related to new families of numbers (2016, background): “[1, 25, 26, 36]; see also the references cited in each of these earlier works).”
- Explicit formulas for p-adic integrals: approach to p-adic distributions and some families of special numbers and polynomials. (2019, background): “[19], [7], [17], [93], [98], [101]; and see also the references cited in each of these earlier works).”
- Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals (2018, background): “[32, 35], and see also the references cited in each of these earlier works).”