Date: Sep 6, 2012 10:43 AM
Author: ksoileau
Subject: Gamma Function - Bessel Function Identity

I have observed and proved the following identity for all x\ne 0 :$$(I_{k-1}(x) +I_{k+1}(x) )I_{-k}(x) -(I_{-k-1}(x)+I_{-k+1}(x))I_k(x) = \frac{4 k}{x \Gamma (1-k) \Gamma (1+k)}$$Is this well-known or trivially derived? Any comments will be appreciated.Thanks,Kerry M. Soileau