  We review properties of confluent functions and the closely related Laguerre
polynomials, and determine their bilinear integrals. As is well-known, these
integrals are convergent only for a limited range of parameters. However, when
one uses the generalized integral they can be computed essentially without
restricting the parameters. This gives the (generalized) Gram matrix of
Laguerre polynomials. If the parameters are not negative integers, then
Laguerre polynomials are orthogonal, or at least pseudo-orthogonal in the case
of generalized integrals. For negative integer parameters, the orthogonality
relations are more complicated.
