MathGroup Archive 1992

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Re: Integrate bug

  • To: mathgroup at
  • Subject: Re: Integrate bug
  • From: David Withoff <withoff>
  • Date: Sat, 25 Jan 1992 23:49:14 -0600

This bug in definite integration of certain exponential integrands is
caused by an error in the definition of HypergeometricURule at the
rule should be replaced with:

 HypergeometricURule =
  HypergeometricU[a_,b_,z_. E^(2 I arg[c_/;Znak[c]] + r_.)] :>
  E^(-2 I arg[c] b) HypergeometricU[a,b,z E^r] +
  (1 - E^(-2 I arg[c] b)) Gamma[1-b]/Gamma[1+a-b] Hypergeometric1F1[a,b,z E^r],
  HypergeometricU[1,1,z_/;Znak[z]] :> -E^z ExpIntegralEi[-z],
  HypergeometricU[1,1,z_/;!Znak[z]] :> E^z ExpIntegralE[1,z],
  HypergeometricU[1/2,1/2,z_/;!Znak[z]] :> Sqrt[Pi] E^z Erfc[Sqrt[z]],
  HypergeometricU[a_,b_,z_/;!Znak[z]] :> Pi^(-1/2) E^(z/2) z^(1/2-a) *
      BesselK[a-1/2,z/2]/;Expand[b-2 a]===0

The same fix can be entered from top-level using:

    HypergeometricURule = ...

The mistake is present only in some early releases of V2.0.  The fix is
also available by contacting WRI Technical Support, and was posted a few
months ago, so other people may have it if I have inadvertently made a
typo in the above.

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