Problems on definit integratiion of gaussian profiles
- To: mathgroup at smc.vnet.net
- Subject: [mg86785] Problems on definit integratiion of gaussian profiles
- From: Regaly Zsolt <regaly at konkoly.hu>
- Date: Fri, 21 Mar 2008 01:51:53 -0500 (EST)
Dear All Mathgroup Fellows! I dont understand the behavoir of Mathematica integrating exponential functions. I try to integrate the same functions in different forms. The integrands are Power[E, Plus[Times[-1, Power[a, 2], Power[c, -2]], Times[-1, Power [d, -2], \ Power[Plus[b, Times[-1, x]], 2]]]] or Power[E, Plus[Times[-1, Power[a, 2], Power[c, -2]], Times[-1, Power [b, 2], \ Power[d, -2]], Times[2, b, Power[d, -1], x], Times[-1, Power[d, -2], Power[x, \ 2]]]] which are the same, but the results will differ. Indeed calculating definit integral in a -Infinity to Infinity domain, assuming that all variables are larger than 0, the result will be completly different! 1'st case the result will be: Times[d, Power[E, Times[-1, Power[a, 2], Power[c, -2]]], Power[Pi, \ Rational[1, 2]]] while in the 2'nd case Times[d, Power[E, Plus[Power[b, 2], Times[-1, Power[a, 2], Power[c, -2]], \ Times[-1, Power[b, 2], Power[d, -2]]]], Power[Pi, Rational[1, 2]]] As You can see the 1'st result is completly independent of b! I dont understand. How can it be fixed? Cheers, Zsolt Regaly