Related papers: Numerical Calculation of Bessel Functions
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
The exponentially convergent trapezoidal rule is applied to a suitable integral representation of the Faddeeva function to derive a simple formula for its evaluation. I describe its properties, strategies for maximising its efficiency, and…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel function is discussed in terms of the solution of the fractional…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
A new formula is derived that generalises an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, $P_l^m(x)$, of degree $l$ and order…
We present formulas for accurate numerical conversion between functions represented by multiwavelets and their multipole/local expansions with respect to the kernel of the form, $e^{\lambda r}/r$. The conversion is essential for the…
This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded into…
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global H\"older and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
Oscillating integrals often arise in the theoretical description of phenomena in chemical physics, in particular in atomic and molecular collisions, and in spectroscopy. A computer code for the numerical evaluation of the oscillatory…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…