  We show that a certain spectral sum of the product of two triple product
integrals of automorphic forms (where the first factor involves the classical
theta-function, a fixed Maass cusp form $u_1$ of weight 0 and a varying Maass
cusp form of weight 1/2 , and the second factor is similar, but contains
another fixed Maass cusp form $u_2$ of weight 0 in place of $u_1$) can be
expressed as an integral involving the Rankin-Selberg L-function of $u_1$ and
$u_2$. In the special case $u_1$ = $u_2$ our formula reduces to a spectral
reciprocity identity which (in slightly different form) was proved recently by
Humphries-Khan ([H-K]) and Kwan ([Kw]).
