相关论文: A solution to an open problem on the Mathieu serie…
Motivated by several generalizations of the well--known Mathieu series, the main object of this paper is to introduce new extension of generalized Mathieu series and to derive various integral representations of such series. Finally master…
An open problem concerning Riemann sums, posed by O. Furdui, is considered.
While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short…
In this paper we give a closed expression for a multiple factorial series, solving Open Problem 3.137 in a recent book by O. Furdui. The method is based on properties of divided differences. It applies also to similar series and certain…
Inequalities, asymptotics and, for some specific cases, asymptotical expansions were obtained for generalized Mathieu's series. A connection between inequalities for Mathieu's series and positive definite and completely monotonic functions.
We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.
The main purpose of this paper is to present closed integral form expressions for the Mathieu-type $\boldsymbol a$-series and its associated alternating version whose terms contain a $(p, q)$-extended Gauss' hypergeometric function. Certain…
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In this paper we obtain a new parametric solution of the problem of finding two triads of biquadrates with equal sums and equal products.
Let G be a finite abelian group of order n. For a complex valued function f on G, let \fht denote the Fourier transform of f. The uncertainty inequality asserts that if f \neq 0 then |supp(f)| |supp(\fht)| \geq n. Answering a question of…
Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \begin{align*} \bigg\| \,\int_{B(0,\cdot)} f \cdot \int_{B(0,\cdot)} g \,\bigg\|_{q,u,(0,\infty)} & \leq C \, \|f\|_{p_1,v_1,{\mathbb R}^n}…
In the present paper, a general theory for the second-order matrix difference equation of bilateral type is discussed. We introduced the matrix $q$-Kummer equation of bilateral type and presented the $q$-Kummer matrix function as a series…
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by…
In this paper, we use some Fourier analysis techniques to find an exact solution to the Cauchy problem for the $n$-dimensional biwave equation in the upper half-space $\mathbb{R}^n\times [0,+\infty)$.
Our aim in this paper is to show some new inequalities for Mathieu's type series and Riemann zeta function. In particular, some Tur\'an type inequalities, some monotonicity and log-convexity results for these special functions are given.…
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.
We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the…
We construct a family of $q$-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $\mathbb{Q}$-valued solution of the extended double shuffle equations. These…
This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace…