Abstract
In this work, we discuss several desirable properties of the inverse Gaussian (IG) family involving orthogonal polynomials. In particular, we discuss the cumulant-generating function and associated polynomials. A particularly important property is that the associated polynomials satisfy a four-term recurrence relation. Then we state and calculate the famous creation and annihilation operators of the Heisenberg-Weyl Lie algebra that acting on IG polynomials Pn as the multiplicative operator X and the derivative one D on the monomials xn . Finally, I used the Maple computer algebra system to program and Calculate the six first IG polynomials and their roots numerically.
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