相关论文: A note on trigonometric approximations of Bessel f…
Several sums of Neumann series with Bessel and trigonometric functions are evaluated, as finite sums of trigonometric functions. They arise from a generalization of the Neumann expansion of the eigenstates of the Laplacian in regular…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
In this work, series expansions in terms of Bessel functions of the first kind are given for the sine and cosine integrals. These representations differ from many of the known Neumann-type series expansions for the sine and cosine…
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums…
We establish the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, including the mapping relations between power series and trigonometric series,…
We have discovered three non-power infinite series representations for Bessel functions of the first kind of integer orders and real arguments. These series contain only elementary functions and are remarkably simple. Each series was…
We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
In this paper we derive a new class of sum rules for products of the Bessel functions of first kind. Using standard algebraic manipulations we extend some of the well known properties of $J_n$. Some physical applications of the results are…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann…
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral…
A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to the spectral parameter. For the…
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…
Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…
In this paper, we are interested in a Neumann-type series for modified Bessel functions of the first kind which arises in the study of Dunkl operators associated with dihedral groups and as an instance of the Laguerre semigroup constructed…
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
Infinite series of Bessel function of the first kind, $\sum_\nu^{\pm\infty} J_{N\nu+p}(x)$, $\sum_\nu^{\pm\infty} (-1)^\nu J_{N\nu+p}(x)$, are summed in closed form. These expressions are evaluated by engineering a Dirac comb that selects…
In this paper we consider a sum of modified Bessel functions of the first kind of which particular case is used in the study of Kanter's sharp modified Bessel function bound for concentrations of some sums of independent symmetric random…