  The integral representations for the eigenfunctions of $N$ particle quantum
open and periodic Toda chains are constructed in the framework of Quantum
Inverse Scattering Method (QISM). Both periodic and open $N$-particle solutions
have essentially the same structure being written as a generalized Fourier
transform over the eigenfunctions of the $N-1$ particle open Toda chain with
the kernels satisfying to the Baxter equations of the second and first order
respectively. In the latter case this leads to recurrent relations which result
to representation of the Mellin-Barnes type for solutions of an open chain. As
byproduct, we obtain the Gindikin-Karpelevich formula for the Harish-Chandra
function in the case of $GL(N,\RR)$ group.
