2ND-ORDER STATISTICS OF INTEGRATED-INTENSITIES AND DETECTED PHOTONS, THE EXACT ANALYSIS .1. THEORY

We express the exact probability density distribution function as the product of a gamma distribution and a series of associated Laguerre po lynomials, with the expansion coefficients determined by moments of th e integrated intensity. Orthogonal polynomials with respect to the exa ct probability distribution function are then expanded in similar fash ion. These polynomials are then used to construct an expansion of the joint probability distribution function in the second-order photoelect ron statistics. Since the polynomials are identical with the correspon ding Laguerre polynomials when the exact probability distribution func tion is the gamma distribution, the new polynomials are generalized ve rsions of the associated Laguerre polynomials. The joint photoelectron statistics may be studied with these new polynomials.