On the Carlitz expansion in products of Bessel functions (Q689890)

This paper resolves the Carlitz series case of the general problem investigated in the preceding paper in the volume [\textit{H. Langer}, \textit{R. Mennicken}, the author and \textit{A. Sattler}, ibid. 24, 129-146 (1993; see the preceding review)]. The Carlitz series \(\bigl({z\over 2}\bigr)^{\nu+\mu}= \sum^ \infty_{n=0} c_ n J_{\mu+n}(az)J_{\nu+n}(bz)\) is realized as the first component of the simultaneous expansion of a pair of functions in terms of Bessel functions, this being related to eigenfunction expansions associated with a \(4\times 4\) first order differential system.