This is a research question for which I am not able to find any existing reference. So, I am reaching out for help. The project is related to studying the sequence of rejections in multiple hypothesis testing. But I cannot give out details on my strategy.

However, a key step is to obtain orthogonal polynomial expansion for bi-variate noncentral chi-square and bi-variate noncentral student t distribution. I have searched online but was only able to find such expansion for univariate non-central chi-square and univariate non-central student t distribution.

I would greatly appreciate if you can point out a general method (or reference, if existent) to construct orthogonal polynomials with respect to bi-variate densities (different thant that given by G. K. Eagleson's "Polynomial expanions of bivariate distributions" and Meixner's paper cited therein, since the methods there do not seem to work for bi-variate non-central chi-square or student t distribution). Thank you in advance.

Best regards, Chee


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