Incorrect FullSimplify result involving BesselK functions
- To: mathgroup at smc.vnet.net
- Subject: [mg8110] Incorrect FullSimplify result involving BesselK functions
- From: Josip Loncaric <josip at icase.edu>
- Date: Tue, 12 Aug 1997 00:54:50 -0400
- Organization: ICASE
- Sender: owner-wri-mathgroup at wolfram.com
FullSimplify in Mathematica 3.0 incorrectly simplifies the following expression to zero: bk = BesselK[-1 + n, r] + (2*n*BesselK[n, r])/r + BesselK[1 + n, r] FullSimplify[bk] 0 Zero is inconsistent with the numerical result: N[bk /. n -> 3/2 /. r -> 1] 6.45496 When n=1/2, 3/2, 5/2, ... the correct expression for bk can be obtained in analytic form via regular Simplify function. For example, one obtains Simplify[bk /. n->3/2 ] (Sqrt[2*Pi]*(3 + 3*r + r^2))/(E^r*r^(5/2)) N[% /. r->1] 6.45496 The corresponding BesselI expression does not suffer from this particular bug: bi = BesselI[-1 + n, r] + (2*n*BesselI[n, r])/r + BesselI[1 + n, r] simplebi = FullSimplify[bi] 2*BesselI[-1 + n, r] N[bi /. n -> 3/2 /. r -> 1] 1.87535 N[simplebi /. n -> 3/2 /. r -> 1] 1.87535 Anyone working with cylindrical functions can be bitten by this serious bug. A possible source of this problem is the fact that some textbooks forget that the recurrence relations for modified Bessel functions do not apply to BesselK directly but to Exp[I*n*Pi]*BesselK[n,r] so that a sign change is involved (unlike the BesselI function which does not require a sign change). Is there a workaround? -- Dr. Josip Loncaric, Senior Staff Scientist ICASE, M/S 403, NASA Langley Research Center, Hampton, VA 23681-0001 Phone: (757) 864-2192 mailto:josip at icase.edu Fax: (757) 864-6134 http://www.icase.edu/~josip/