Journal ArticleDOI
Automatic Computation of Zeros of Bessel Functions and Other Special Functions
TLDR
An efficient algorithm is developed for the automatic calculation of the zeros of Bessel functions of arbitrary order, Coulomb wave functions, and other special functions without any actual functional evaluations.Abstract:
An efficient algorithm is developed for the automatic calculation of the zeros of Bessel functions of arbitrary order, Coulomb wave functions, and other special functions. Remarkably, this can be done without any actual functional evaluations. Limitations and generalizations are discussed.read more
Citations
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Book
A fast algorithm for the calculation of the roots of special functions
TL;DR: A procedure for the determination of the roots of functions satisfying second-order ordinary differential equations, including the classical special functions, is described, based on a combination of the Prufer transform with the classical Taylor series method.
Journal ArticleDOI
The Zeros of Special Functions from a Fixed Point Method
TL;DR: The structure of the first order difference-differential equations (DDEs) is studied to set global bounds on the differences between adjacent zeros of functions of consecutive orders and to find iteration steps which guarantee that all the zeros inside a given interval can be found with certainty.
Journal ArticleDOI
Zeros of the Macdonald function of complex order
Erasmo Ferreira,Javier Sesma +1 more
TL;DR: In this paper, the z-zeros of the modified Bessel function of the third kind K"@n(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order @n.
Journal ArticleDOI
CCOMP: An efficient algorithm for complex roots computation of determinantal equations
TL;DR: A free Python algorithm, entitled CCOMP (Complex roots COMPutation), is developed for the efficient computation of complex roots of determinantal equations inside a prescribed complex domain through the efficient determination of the candidate points inside the domain which, in their close neighborhood, a complex root may lie.
Journal ArticleDOI
Space-time dependency modeling using general classes of flexible stationary variogram models
TL;DR: In this paper, the authors describe a generalization of the Shapiro and Botha approach for the case of anisotropy in two components with a view to obtaining flexible stationary variogram models suitable for modeling spatiotemporal dependency.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
A treatise on the theory of Bessel functions
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Book
Mathematics for the Physical Sciences
TL;DR: In this paper, the authors proposed a mathematical approach for the physical sciences for the purpose of mathematics for physical sciences, which is based on the idea of mathematics in the physical domain.