Related papers: Note on the truncated generalizations of Gauss' sq…
We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…
We provide evidence for a conjecture of Yamamura that the truncated logarithmic polynomials \[ F_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n} \] have Galois group $S_n$ for all $n \geq 1$.
The long-wavelength approximation and the truncated Taylor expansion are frequently used in the theory of relativistic Coulomb excitation to obtain multipole expansions of the interaction. It is shown in this note that these two…
In 2012, Andrews and Merca obtained a truncated version of Euler's pentagonal number theorem and showed the nonnegativity related to partition functions. Meanwhile, Andrews-Merca and Guo-Zeng independently conjectured that the truncated…
Expressions are given for the truncated fractional moments $E X_+^p$ of a general stable law. These involve families of special functions that arose out of the study of multivariate stable densities and probabilities. As a particular case,…
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
We prove, combinatorially, that the product of a Schubert polynomial by a Stanley symmetric polynomial is a truncated Schubert polynomial. Using Monk's rule, we derive a nonnegative combinatorial formula for the Schubert polynomial…
This research investigates the relations between the fixed points of asymptotically contractive operators defined on complete liner metric spaces, in general, and in separable Hilbert spaces in particular and their obtained truncations of…
As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.
We give a complete description of the set of extended eigenvectors of truncated shifts defined on the model spaces K_u := H^2\ominus uH^2, in the case of u is a Blaschke product.
Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing, and is typically only feasible using approximate MCMC sampling. In this article we propose a minimax tilting…
In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of…
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…
We propose an expansion of the unitary evolution operator, associated to a given Schr\"odinger equation, in terms of a finite product of explicit unitary operators. In this manner, this unitary expansion can be truncated at the desired…
A number of new terminating series involving $\sin(n^2/k)$ and $\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are…
We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some…
We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…
The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon is proved to be the generic Newton polygon of the twisted $C$-function of the T-adic exponential sum. It gives the…