TITLE: Diagonalization of the matrix $(1/(i+j+\rm{const}))_{i,j}$
QUESTION [6 upvotes]: 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 $t$?

REPLY [10 votes]: See "On the Hilbert matrix II" by Rosenblum