Airy and Bessel functions for complex argument
- To: mathgroup at yoda.physics.unc.edu
- Subject: Airy and Bessel functions for complex argument
- From: Todd Pitts <todd at wombat.ee.byu.edu>
- Date: Wed, 25 Sep 91 15:40:24 mdt
I am using version 1.2 of mathematica for the HP workstation. I am having trouble
with the Airy function and have traced the problem to the Bessel's which may be used to
represent the Airy function.
Plot[AiryAi[x],{x,-10,10}]
works fine. However
D[AiryAi[x],x]
Plot[%,{x,-10,10}]
produces an incorrect plot. Additionally, it calculates COMPLEX values for negative x. I
have tried representing the Airy function via Bessel identities from Abramowitz and Stegun.
This gives similar difficulties whenever the Bessel's are required to handle complex arguments. I
need to be able to work with Ai[x], Bi[x], their derivatives as well as the Bessel functions for
complex arguments. I would appreciate any suggestions. I noticed that in version 2.0 there exists
an AiryAi[],AiryBi[], and functions specifically designed to return their derivatives. This
eliminates some of the difficulties, however I have tried the Bessel representations of the Airy in
2.0 and the same problem still exists when their argument becomes complex.
Todd Pitts