Related papers: Some dual definite integrals for Bessel functions
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
In this paper, on the complex field $\mathbb{C}$, we prove two integral formulae for the Hankel-Mellin transform and the double Fourier-Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications,…
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
The $q$ analog of Modified Bessel functions and Bessel-Macdonald functions, were defined in our previous work (q-alg/950913) as general solutions of a second order difference equations. Here we present a collection of their representations…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from $n$ nonuniform points to $m$ nonuniform frequencies in $O((m+n)\log\min(n,m))$ operations. Our approach combines local and asymptotic Bessel…
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k Bessel function.…
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
We establish an explicit form of the Backlund transformation for the most known integrable systems.
Making use of Chebyshev polynomials, we obtain upper bound estimate for the second Hankel determinant of a subclass $\mathcal{N}_{\sigma }^{\mu}\left( \lambda ,t\right) $ of bi-univalent function class $\sigma.$
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
We examine convergent representations for the sum of Bessel functions \[\sum_{n=1}^\infty \frac{J_\mu(na) J_\nu(nb)}{n^{\alpha}}\] for $\mu$, $\nu\geq0$ and positive values of $a$ and $b$. Such representations enable easy computation of the…
We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.