The following function computes the logarithm of the modified Bessel function of the 1st kind I(nu, z). It uses the scipy method and extends it when it is not tractable, using 2 different methods (1 ...
Several second order ODEs of the form 𝒚 ′′ + 𝒑(𝒙)𝒚 ′ + 𝒒(𝒙)𝒚 = 𝒓(𝒙) are of practical importance have Power series solution if coefficients p(x), q(x) and r(x) are functions instead of ...
Geometric Function Theory is a vibrant field that investigates the geometric properties of analytic functions, including univalence, starlikeness, and convexity, which are key to understanding their ...
THE function to which these volumes are devoted received its name from the astronomer Bessel, 1824, on introducing it for the coefficients in the expansion of radius vector, and true or eccentric ...
Abstract: This appendix talks about Bessel functions. Zeros of the ordinary Bessel function and its derivative can be approximated by the first two terms of McMahon's expansion. The chapter shows the ...
A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass ...
Copyright © 2014 by author and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). A ...
Abstract: New approximate solutions to the v-order Bessel function of the first kind are derived. The solution is expressed as a polynomial for Bessel function of all fractional order polynomial.
Using an integral representation for the first kind Hankel (Hankel-Bessel Integral Representation) function we obtain the so-called Basset formula, an integral representation for the second kind ...
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