2014•Integral Transforms and Special FunctionsRequires access

A note on some relation formulae involving Bessel functions

Juan Luis González‐Santander

Abstract

In the literature, we find a formula relating the modified Bessel functions Iν(z) and Kν(z) that only seems to work for arg z≤0. We provide a formula for any complex number z. This derivation allows us to obtain some new formulae involving, in the one hand, Bessel functions of the second kind Yν(z) and, in the other hand, the spherical modified Bessel functions, in(z) and kn(z).

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Key concepts: Bessel function, Bessel polynomials, Bessel process, Struve function, Mathematics, Cylindrical harmonics, Bessel's inequality, Pure mathematics