Binomial polynomial - Open Access .click

2013
In this chapter we will be primarily interested in the study of monomials and polynomials within the framework of quaternion analysis. Monomials and their applications to combinatorics and number theory have become increasingly important for the study of a large number of problems that arise in many different contexts, both from a theoretical and a ...
Wolfgang Sprößig, Svetlin G. Georgiev, João Morais +2 more
openaire +2 more sources

Binomial formula for Macdonald polynomials and applications [PDF]

Mathematical Research Letters, 1997
The author gives the non-evident and the very non-trivial generalization of the Macdonald polynomials. He defines the ``interpolation Macdonald polynomial'' \(P^*(x_1,\dots, x_n;q,t)\) (\(q\) and \(t\) are two parameters) by the following conditions: (1) \(P^*\) is symmetric in variables \(x_i t_i^{-1}\), (2) \(\deg P_\mu^*=| \mu|\) for any partition \(
openaire +2 more sources

Binomial Sums with Pell and Lucas Polynomials

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2021
Binomial sums with Pell and Lucas polynomials as weight functions are explicitly evaluated. Their special cases result in several interesting identities concerning Fibonacci and Lucas numbers. Two of them confirm the summation formulae proposed recently by Ohtsuka and Tauraso (2020).
Dongwei Guo, Wenchang Chu
openaire +2 more sources

Polynomials of Binomial Type and Renewal Sequences

Studies in Applied Mathematics, 1987
We study polynomials of binomial type that have an exponential generating function of the form { 1 − f(u)−x}. They have a close connection with renewal sequences. The asymptotic behavior as n − ∞ is studied.
openaire +2 more sources

binomial coefficient
pure mathematics
discrete mathematics

combinatorics
mathematical analysis
poisson distribution

negative binomial distribution
physics
binomial theorem