This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac–Mora characterization of the real natural exponential families having cubic variance function.
"Characterization of the cubic exponential families by orthogonality of polynomials." Ann. Probab. 32 (3B) 2463 - 2476, July 2004. https://doi.org/10.1214/009117904000000522