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.