# Arbitrary precision BesselY

Hi, I consider using Sage for some calculations which contain Bessel functions of complex arguments. Since I have to mix Bessel functions with very small and very large arguments I require precision higher than 15 digits.

Unfortunately, I recognized that BesselY is not implemented in PARI. But BesselJ and BesselH1 are. My physicists understanding of math tells me, I could just use "(BesselH1-BesselJ)/i". But I am surprised that this has not been discussed before (at least I couldn't find it), since this would allow a quick implementation of BesselY. Am I missing something that's obvious for math experts? Or can I just use above definition to get an arbitrary precision BesselY?

Many thanks Frank