Consider the following infinite matrix: $A\_{i,j}=\frac1{i+j+\gamma}$, $0\leq i,j<\infty$, $\gamma>0$ is a constant. Is it known how to diagonalize $A$, or, say, calculate $(I+tA)^{-1}$ for parameter $t$?



Diagonalization of the matrix $(1/(i+j+\rm{const}))_{i,j}$
See ["On the Hilbert matrix II"](http://www.ams.org/journals/proc/1958-009-04/S0002-9939-1958-0099599-2/) by Rosenblum


