相关论文: Analytical results for a Bessel function times Leg…
Let $f_{\bf c}(r)=\sum_{n=0}^\infty e^{c_n}r^n$ be an analytic function; ${\bf c}=(c_n)\in l_\infty$. We assume that $r$ is some logarithmically convex and lower semicontinuous functional on a locally convex topological space $L$. In this…
Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [23]). For numerically solving TFDEs, two kinds of generalized Laguerre functions were defined and some…
Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
An expansion procedure using third kind Chebyshev polynomials as base functions is suggested for solving second type Volterra integral equations with logarithmic kernels. The algorithm's convergence is studied and some illustrative examples…
We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube…
Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ is the imaginary unit, and…
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…
Special values of the Lommel functions allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
The solution in hyperspherical coordinates for $N$ dimensions is given for a general class of partial differential equations of mathematical physics including the Laplace, wave, heat and Helmholtz, Schr\"{o}dinger, Klein-Gordon and…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture…
We derive an asymptotic error formula for Gauss--Legendre quadrature applied to functions with limited regularity, using the contour-integral representation of the remainder term. To address the absence of uniformly valid approximations of…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…
In this paper, we investigate approximate solutions for nonlinear Fredholm integro-differential equations of fractional order. We present an operational Tau method by obtaining the Tau matrix representation. We solve a special class of…