Hadamard Integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg72136] Hadamard Integration*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Wed, 13 Dec 2006 06:39:51 -0500 (EST)

Dear All, The following is about a two dimensional integral that appeared on a private communication with a member of the forum. Known constants: params = {k -> 0.1, a -> 1, M -> 0.3, Deltax1 -> 1}; e1 = 1; b = Sqrt[1 - M^2]; x0 = a/2; h is the variable of integration of the external integral (the regular one). y0 = -h; z0 = 0; r = Simplify[Sqrt[y0^2 + z0^2], h > 0] R = Sqrt[x0^2 + b^2*r^2] X = (x0 - M*R)/b^2 X1 = Sqrt[X^2 + r^2] The Hadamard integral is the internal integral with variable of integration u. ff = (1/(8*Pi))*(Deltax1*NIntegrate[((M*E^(I*k*X))/(R*X1) + NIntegrate[E^(I*k*u)/(r^2 + u^2)^(3/2), {u, -Infinity, Plus[X]}])/ E^(I*k*x0), {h, -e1, Plus[e1]}]) Some work has already be done on ii but I really appreciate any assistance! Best Regards Dimitris