Topic
Abel polynomials
About: Abel polynomials is a research topic. Over the lifetime, 27 publications have been published within this topic receiving 1439 citations.
Papers
TL;DR: Using notions of composita and composition of generating functions, the authors obtained explicit formulas for Chebyshev polynomials, the Legendre polynomial, the Gegenbauer polynomorphism, the Associated Laguerre poynomials (ALP), the Stirling polynomic, the Abel polynomalization, the Bernoulli polynomials of the second kind, the Generalized Bernoullians of the Second Kind, the Euler Polynomials, and the Peters polynomenials.
52 citations
TL;DR: A special case of the Abel polynomials counts rooted labeled forests and this interpretation is used to obtain a combinatorial proof of the formula expressing x^n as a sum of these polynmials.
27 citations
TL;DR: In this article, the identities of Bernoulli, Euler, and Abel polynomials arising from umbral calculus were derived for the Euler polynomial, and some identities of Euler and Abel were derived as well.
Abstract: In this paper, we derive some identities of Bernoulli, Euler, and Abel polynomials arising from umbral calculus.
18 citations
TL;DR: In this article, a two-parameter class of discrete distributions, Abel series distributions, generated by expanding a suitable pa,rametric function into a series of Abel polynomials is discussed.
Abstract: A two-parameter class of discrete distributions, Abel series distributions, generated by expanding a suitable pa,rametric function into a series of Abel polynomials is discussed An Abel series distribution occurs in fluctuations of sample functions of stochastic processes and has applications in insurance risk, queueing, dam and storage processes The probability generating function and the factorial moments of the Abel series distributions are obtained in closed forms It is pointed out that the name of the generalized Poisson distribution of Consul and Jain is justified by the form of its generating function Finally it is shown that this generalized Poisson distribution is the only member of the Abel series distributions which is closed under convolution
18 citations
Posted Content•
TL;DR: In this article, the authors provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting.
Abstract: We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution.
17 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 2 |
| 2014 | 1 |
| 2013 | 4 |
| 2010 | 2 |
| 2009 | 2 |