Related papers: An inequality regarding differential polynomial
In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.
In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
Some Open Problems Concerning Orthogonal Polynomials.
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
We prove the stronger version of Harnack's inequality for positive harmonic functions defined on the unit disc.
We obtain simple proofs of certain inequalites for bivariate means.
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
We prove a Poincare type inequality for differential forms on compact manifolds by means of a constructive 'globalization' of a local Poincare inequality on convex sets.
We consider inequalities of Bombieri type for polynomials that need not be homogeneous, using the apolar inner product.
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.
For each positive integer $d$, we prove a uniform $l^2$-decoupling inequality for the collection of all polynomials phases of degree at most $d$. Our result is intimately related to \cite{MR4078083}, but we use a different partition that is…
In the paper we obtain the asymtotic number of integral quadratic polynomials with bounded heights and discriminants as the upper bound of heights tends to infinity.
Lower bounds are given for the number of non-real zeros of a second order linear differential polynomial with constant coefficients in a real entire function with finitely many non-real zeros.