Results 271 to 280 of about 582,984 (315)

Ruin probability for finite negative binomial mixture claims via recurrence sequences

Communications in Statistics - Theory and Methods, 2022
A new procedure to find the ultimate ruin probability in a discrete-time risk model is presented for claims with a mixture of m negative binomial distributions. The method involves the theory of linear recurrence sequences. It requires to find the zeroes
Luis Rincón, David J. Santana
semanticscholar   +1 more source

Binomial Sums with Pell and Lucas Polynomials

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2021
Pell and Pell-Lucas polynomials are given recursively by \(P_n(x)=2xP_{n-1}(x)+P_{n-2}(x)\) and \(Q_n(x)=2xQ_{n-1}(x)+Q_{n-2}(x)\), respectively, with initial conditions \(P_0(x)=0, P_1(x)=1, Q_0(x)=2, Q_1(x)=2x\). They generalize the Fibonacci and Lucas numbers, which correspond to \(F_n=P_n(\frac 12)\) and \(L_n=Q_n(\frac 12)\), respectively.
Guo, Dongwei, Chu, Wenchang
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Moment functions of higher rank on polynomial hypergroups

Advances in Operator Theory, 2022
In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures.
Ż. Fechner, E. Gselmann, L'aszl'o Sz'ekelyhidi   +2 more
semanticscholar   +1 more source

Polynomial Sequences of Binomial Type Path Integrals

Annals of Combinatorics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. Kisil
semanticscholar   +3 more sources

Binomial-Weighted Orthogonal Polynomials

Journal of the ACM, 1967
This paper discusses a set of polynomials, {φ r ( s )}, orthogonal over a discrete range, with binomial distribution, b ( s ; n , p ), as the weighting function.
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Monomials, Polynomials and Binomials

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 ...
João Pedro Morais, Svetlin Georgiev, Wolfgang Sprößig   +2 more
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q-Parikh Matrices and q-deformed binomial coefficients of words

Discrete Mathematics
We have introduced a q-deformation, i.e., a polynomial in q with natural coefficients, of the binomial coefficient of two finite words u and v counting the number of occurrences of v as a subword of u.
Antoine Renard, M. Rigo, Markus Alan Whiteland   +2 more
semanticscholar   +1 more source

A study of monogenity of binomial composition

Acta Arithmetica
Let θ be a root of a monic polynomial h(x)∈Z[x] of degree n≥2. We say that h(x) is monogenic if it is irreducible over Q and {1,θ,θ2,…,θn−1} is a basis for the ring ZK of integers of K=Q(θ).
A. Jakhar, R. Kalwaniya, Prabhakar Yadav
semanticscholar   +1 more source

Diophantine equations with truncated binomial polynomials

Indagationes Mathematicae, 2016
The authors consider the Diophantine equation \(P_{n,k}(x)=P_{m,\ell}(y)\) in integers \(x,y\), where, for positive integers \(k\leq n\), \(P_{n,k}(x)=\sum_{j=0}^k {n\choose j}x^j\) is a truncated binomial expression of \((1+x)^n\). Under certain irreducibility assumptions, they show that the equation admits only finitely many solutions.
Dubickas, Artūras, Kreso, Dijana
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The Characteristic Polynomial of a Certain Matrix of Binomial Coefficients

The Fibonacci quarterly, 1965
A n + 1 = [] (r. s = 0, 1,. .. . n). a m a t r i x of o r d e r n+1; for example A , 0 0 0 1 0 0 1 1 0 1 2 1 1 3 3 1 Let (1.2) £ n + 1 (x) = " d e t (x I-A n + 1) denote the c h a r a c t e r i s t i c polynomial of A ,.
L. Carlitz
semanticscholar   +1 more source