MathGroup Archive 1991

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Airy and Bessel functions for complex argument

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  • Subject: Airy and Bessel functions for complex argument
  • From: Todd Pitts <todd at>
  • 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.  

works fine.  However 
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

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