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Re: Integrate bug
*To*: mathgroup at yoda.physics.unc.edu
*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:
BeginPackage["Integrate`"]
Clear[HypergeometricURule]
HypergeometricURule = ...
EndPackage[]
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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