Abstract
The Jacobi–Stirling numbers of both kinds are specializations of elementary and complete homogeneous symmetric functions. We use this fact to discover and prove some algebraic identities involving Jacobi–Stirling numbers. The Legendre–Stirling numbers are very special cases of the Jacobi–Stirling numbers. New connections between the Legendre–Stirling numbers and the central factorial numbers of odd indices are presented.
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