Related papers: Numerical Calculation of Bessel Functions
This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the…
In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…
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…
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
In this paper, we determine necessary and sufficient conditions for the generalized Bessel function to be in certain subclasses of starlike and convex functions. Also, we obtain several corollaries as special cases of the main results,…
Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite intervals is described. The procedure is useful, for instance, to…
We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…