Related papers: Partial sums of Hyper-Bessel function with applica…
In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…
In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact…
We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.
Starting from the addition formula for little $q$-Jacobi polynomials, we derive a new addition formula for the little $q$-Bessel functions. The result is obtained by the use of a limit transition. We also establish a product formula for…
In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concepts of superterzatic functions.
The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…
In this paper, we consider the fractional sum of the divisor functions. We can improve previous results considered by Bordell\'{e}s \cite{Bo} and Liu-Wu-Yang \cite{LWY}.
The order derivatives of the modified Bessel function of the second kind at s = .5 are obtained as finite expressions of integrals that generalize the exponential integral appearing in the first derivative (Theorem 1.) The derivatives arise…
Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for…
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…
Our purpose in this present paper is to investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ to obtain the results in representation of Wright-type function. Also, we establish certain…
In the present work, we propose to investigate the second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting applications of the results presented here are also discussed.
In this paper we consider fractional quasi-Bessel equations $$\sum_{i=1}^{m}d_i x^{\alpha_i+p_i}D^{\alpha_i} u(x) + (x^\beta - \nu^2)u(x)=0$$ and construct their existence and uniqueness theory in the class of fractional series. Our…
In this paper we establish the generalized Beukers integral $I_{m}(a_{1},...,a_{n})$ with some methods of partial fraction decomposition. Thus one obtains an explicit expression of the generalized Beukers integral. Further, we estimate the…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.