Moments of the free Jacobi process: a matrix approach

Nizar Demni, Tarek Hamdi

Published 2024-04-17Version 1

We compute the large size limit of the moment formula derived in \cite{DHS} for the Hermitian Jacobi process at fixed time. In particular, we identify the terms contributing to the limit and show they satisfy a double recurrence relation. We also determine explicitly some of them and revisit a special case relying on Carlitz summation identity for terminating $1$-balanced ${}_4F_3$ functions taken at unity.