Related papers: Generalizations of a theorem about the binomial co…

We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these…

We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

In this paper we give a generalization of a result of Wei.

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…

In this paper, we generalize Gauss' lemma for polynomials over subtractive factorial semidomains.

We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.

A generalization of the law of total covariance is presented and proved.

In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…

We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…

The Concepts of poly-Bernoulli numbers $B_n^{(k)}$, poly-Bernoulli polynomials $B_n^{k}{(t)}$ and the generalized poly-bernoulli numbers $B_{n}^{(k)}(a,b)$ are generalized to $B_{n}^{(k)}(t,a,b,c)$ which is called the generalized…

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…