On Basic Fourier-Bessel Expansions
Copyright policy )On Basic Fourier-Bessel Expansions
When dealing with Fourier expansions using the third Jackson (also known as Hahn-Exton) $q$-Bessel function, the corresponding positive zeros $j_{kν}$ and the "shifted" zeros, $qj_{kν}$, among others, play an essential role. Mixing classical analysis with $q$-analysis we were able to prove asymptotic relations between those zeros and the "shifted" ones, as well as the asymptotic behavior of the third Jackson $q$-Bessel function when computed on the "shifted" zeros. A version of a $q$-analogue of the Riemann-Lebesgue theorem within the scope of basic Fourier-Bessel expansions is also exhibited.
basic hypergeometric function, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), third Jackson \(q\)-Bessel function, basic Fourier-Bessel expansions, Riemann-Lebesgue theorem, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), 42C10, 33D45, 33D15, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hahn-Exton \(q\)-Bessel function, asymptotic behavior
basic hypergeometric function, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), third Jackson \(q\)-Bessel function, basic Fourier-Bessel expansions, Riemann-Lebesgue theorem, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), 42C10, 33D45, 33D15, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hahn-Exton \(q\)-Bessel function, asymptotic behavior
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