1 Jan 09:00 2002

### integrate bessel_k(2,%i*y) surprise

Edwin Woollett <woollett <at> charter.net>

2002-01-01 08:00:23 GMT

2002-01-01 08:00:23 GMT

I am just playing around with bessel_k and don't understand the large imaginary part of the integral of bessel_k(2, %i*y) over the interval 1 <= y <= 100, based on the table of discrete values displayed below: (f(x) is just fchop(expand(float(x))) ) -------------------------------- (%i1) load(nint); (%o1) "c:/work2/nint.mac" (%i25) for y:1 step 10 thru 100 do print(" ",y," ",f(bessel_k(2,%i*y)))$ 1 0.18048997206696*%i-2.592886175491198 11 0.21841533174753*%i+0.3119789483129 21 -0.031858737423089*%i-0.27222015896945 31 0.20481495858656-0.093918476739506*%i 41 0.16377581778393*%i-0.10738879820159 51 0.0024786070162412-0.17554486214757*%i 61 0.13641169853138*%i+0.084590710242742 71 -0.064015208750726*%i-0.13429138505077 81 0.13815292462619-0.017659551649835*%i 91 0.084630268914206*%i-0.10051430087896 (%i26) f(integrate(bessel_k(2,%i*y),y,1,100)); (%o26) 1.736293756153568-2.1367387806763253E+42*%i ---------------------------------------------------------------- Where does the 10^42 come from??(Continue reading)