Fixed Point Theory and Applications· 2013Q3
Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications
- 151citations
- Q3SCImago
- 2013year
Short summary
New generating functions are constructed for generalized Stirling type numbers of the second kind, array type polynomials, and Eulerian type polynomials, leading to derived functional and differential equations.
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Key points
- Construction of new generating functions for generalized Stirling type numbers of the second kind, array type polynomials, and Eulerian type polynomials.
- Derivation of functional and differential equations from these generating functions.
- Development of identities such as multiplication formulas and recurrence relations using the derived equations.
- Presentation of applications related to the studied polynomials and numbers.
AI-generated from the title and abstract; the full text is not read.
Abstract
The first aim of this paper is to construct new generating functions for the generalized -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 -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.
The authors' abstract, as published at the source. Fixed Point Theory and Applications, 2013 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics