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