*To*: mathgroup@smc.vnet.net*Subject*: [mg12097] Boundary cond. at Infinity*From*: Edward Goldobin <gold@dresden.isi.kfa-juelich.de>*Date*: Sat, 25 Apr 1998 01:30:29 -0400*Organization*: Research Center Juelich GmbH

I neet to solve diff. equation: DSolve[ { y''[x]-a^2 y[x]==Sinh[x]/Cosh[x]^2, y[0]==0, y[Infinity]==0 },y[x],x ] Math 3.0 complains about boundary condition at "Infinity". Well, I then solve it with boundary cond. at zero only : DSolve[ { y''[x]-a^2 y[x]==Sinh[x]/Cosh[x]^2, y[0]==0 },y[x],x ] And Math.3.0 give me an answer in terms of PolyGamma's and Hypergeometric2F1's with one constant C[2] which I want to find by myself. To find it I need to know the behavior of e.g. Hypergeometric2F1[(1 + a)/2, 1, 1 + (1 + a)/2, -E^(2*x)] at infinity. How can I ask Mathematica to show me the behavior of arbitrary function at infinity? I expect to get something like x*Exp[-2*x] i.e. Taylor is of no use in this case since the behavior is exponential with unknown power. Your help will be appeciated very much. Send a copy of reply by email as well. Thanx