Arbitrary precision BesselY

bessel
pari

asked 2013-01-03 09:52:57 +0200

FrankSt
3 ●2

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

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answered 2013-01-03 10:16:23 +0200

achrzesz
2728 ●5 ●25 ●59

Try:

sage: import mpmath  
sage: mpmath.bessely?

(mpmath is multiprecision package)

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Also note that when http://trac.sagemath.org/sage_trac/ticket/4102 is finished, mpmath will be the default evaluation mode and so asking for as much precision as you want *should* work.