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Problem with NIntegrte

• To: mathgroup at smc.vnet.net
• Subject: [mg47725] Problem with NIntegrte
• From: Joel Storch <jstorch at earthlink.net>
• Date: Fri, 23 Apr 2004 02:31:08 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

y=BesselJ[0,x]/Sqrt[1+x^2]

Integrate[y,{x,-Infinity,Infimity}] yields
  2 BesselI[0,1/2] BesselK[0,1/2] (1.966)

2 NIntegrate[y,{x,0,Infinity},Method->Oscillatory] gives 1.966
(the integrand is an even function)

However,
NIntegrate[y,{x,-Infinity,Infinity},Method->Oscillatory] gives
0.00044788

(Mathematica V5.1)