  In this work we provide a meromorphic continuation in three complex variables
of two types of triple shifted convolution sums of Fourier coefficients of
holomorphic cusp forms. The foundations of this construction are based in the
continuation of the spectral expansion of a special truncated Poincar\'e series
recently developed by Jeffrey Hoffstein. As a result we are able to produce
previously unstudied and nontrivial asymptotics of truncated shifted sums which
we expect to correspond to off-diagonal terms in the third moment of
automorphic L-functions.
