Abstract
Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients. The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain. Zeros of the generated transcendental equation and the relationship of orthogonality are employed to find the unknown coefficients. Several numerical and graphical examples are explained and discussed.
Highlights
Series expansion of single variable functions is represented in Fourier-Bessel form with unknown coefficients
The proposed series expansions are derived for arbitrary radial boundaries in problems of circular domain
Several boundary value problems in the applied sciences are frequently solved by expansions in cylindrical harmonics with infinite terms
Summary
Several boundary value problems in the applied sciences are frequently solved by expansions in cylindrical harmonics with infinite terms. Problems of circular domain with rounded surfaces often generate infinite series of Bessel functions of the first and second types with unknown coefficients. In this case, the intention is to find the series coefficients which should satisfy the boundary conditions. The existence of the origin point excludes Y0(r), Bessel function of the second kind with order zero and argument r, because it goes to negative infinity as r approaches zero [9]
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