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MathGroup Archive 1991

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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






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