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MathGroup Archive 2007

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GenerateConditions->False gives fine result!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73815] [mg73815] GenerateConditions->False gives fine result!
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Fri, 2 Mar 2007 06:06:37 -0500 (EST)

I want to mention one case where GenerateConditions->False gives
desirable result

In[11]:=
Quit

In[1]:=
(1/(2*Pi*I))*Integrate[q*(Exp[(-I)*q*x]/Sqrt[q^2 + t^2]), {q, -
Infinity, Infinity}]
Integrate::idiv: Integral of q/(E^(I*q*x)*Sqrt[q^2 + t^2]) does not
converge \
on {-=E2=88=9E,=E2=88=9E}.
Out[1]=
-((I*Integrate[q/(E^(I*q*x)*Sqrt[q^2 + t^2]), {q, -Infinity,
Infinity}])/(2*Pi))

HOWEVER

In[7]:=
(1/(2*Pi*I))*Integrate[ComplexExpand[q*(Exp[(-I)*q*x]/Sqrt[q^2 +
t^2])], {q, -Infinity, Infinity}, GenerateConditions -> False]
(FullSimplify[#1, t > 0 && x > 0] & )[%]

Out[7]=
-((Sqrt[t^2]*BesselK[1, Sqrt[x^2]/Sqrt[1/t^2]]*Sign[x])/Pi)
Out[8]=
-((t*BesselK[1, t*x])/Pi)

(*check*)

In[24]:=
-((t*BesselK[1, t*x])/Pi) /. {t -> 3, x -> 2}
N[%]
Out[24]=
-((3*BesselK[1, 6])/Pi)
Out[25]=
-0.001283348797177626

In[30]:=
Chop[Block[{Message}, (1/(2*Pi*I))*NIntegrate[q*(Exp[(-I)*q*x]/
Sqrt[q^2 + t^2]) /. {t -> 3, x -> 2}, {q, -Infinity, Infinity}, Method
-> Oscillatory]]]
Out[30]=
-0.0012833487971660698


Dimitris



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