Related papers: Special Bent and Near-bent Functions

We consider a one-parameter family of functions $\{F(t,x)\}_{t}$ on $[0,1]$ and partial derivatives $\partial_{t}^{k} F(t, x)$ with respect to the parameter $t$. Each function of the class is defined by a certain pair of two square matrices…

The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms…

The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…

We review some recent observations in theories with eight supercharges. We point out that such theories can be generalized by starting from the equations of motion rather than from an action. We show that vector multiplets constructed in…

The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…

This work provides calculus for the Fr\'echet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fr\'echet…

Li-Chien Shen developed a family of elliptic functions from the hypergeometric function $_2F_1(\frac{1}{3}, \frac{2}{3} ; \frac{1}{2} ; \bullet)$. We comment on this development, offering some new proofs.

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\chi_d)$, and also of the $L$-functions associated to quadratic twists of an…

We construct uncountably generated algebras inside the following sets of special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere surjective functions and nowhere continuous Darboux functions. All conclusions obtained in this…

We propose a unified approach to $q$-special functions, which are degenerations of basic hypergeometric functions ${}_2\phi_1(a,b;c;q,x)$. We obtain a list of seven different class of $q$-special functions: ${}_2\phi_1, {}_1\phi_1$, two…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

Equivalence classes of Niho bent functions are described for all known types of hyperovals.

By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval's identity.

We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.

Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…

We give a new derivation of the distance-dependent two-point function of planar quadrangulations by solving a new direct recursion relation for the associated slice generating functions. Our approach for both the derivation and the solution…

We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…

In the paper we find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the…

We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…

Dirichlet's $L$-functions are natural extensions of the Riemann zeta function. In this paper we first give a brief survey of Ap\'ery-like series for some special values of the zeta function and certain $L$-functions. Then, we establish two…