Volume 25, pp. 454-466, 2006.

The properties, inequalities and numerical approximation of modified Bessel functions

Juri M. Rappoport


Some new properties of kernels of modified Kontorovitch–Lebedev integral transforms –- modified Bessel functions of the second kind with complex order $ K_{\frac{1}{2}+i\beta }(x) $ are presented. Inequalities giving estimations for these functions with argument $ x $ and parameter $ \beta $ are obtained. The polynomial approximations of these functions as a solutions of linear differential equations with polynomial coefficients and their systems are proposed.

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Key words

Chebyshev polynomials, modified Bessel functions, Lanczos Tau method, Kontorovich-Lebedev integral transforms

AMS subject classifications

33C10, 33F05, 65D20

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