MaplePrimes - answers and comments on Question, BesselJ&BesselY BesselI&BesselK

The general solution of the

edgar — Wed, 10 Mar 2010 20:22:09 Z

The general solution of the Bessel equation is f(x) = A*BesselJ(v,x)+B*BesselY(v,x) where A and B are arbitrary constants. So perhaps the particular f you need has some additional information to let you determine A and B for your case. For example, if you know that f is continuous at 0, then B=0. (I assumed v is an integer.) --- G A Edgar

Thank you

lei_xiaowen — Tue, 16 Mar 2010 05:43:25 Z

Thank you

BesselJ and BesselY

Robert Israel — Wed, 10 Mar 2010 22:47:22 Z

In other words, BesselJ(v,x) and BesselY(v,x) form a basis for the solutions of the Bessel equation. One way of characterizing which of these solutions is BesselJ and which is BesselY is in terms of the asymptotics as x -> infinity:

BesselJ(v,x) ~ sqrt(2*Pi/x)*cos(x - Pi/4 - v*Pi/2) + O(x^(3/2))

BesselY(v,x) ~ sqrt(2*Pi/x)*sin(x - Pi/4 - v*Pi/2) + O(x^(-3/2))