Inversions relating Stirling, tanh, Lah numbers and an application to Mathematical Statistics [article]

G. Della Riccia
2004 arXiv   pre-print
Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if shifted-gamma probability densities and negative binomial distributions are matched by equating their first
more » ... semi-invariants (cumulants), then the cumulants of the two distributions are related by a pair of reciprocal linear combinations equivalent to the inversion formulas established in the first part.
arXiv:math/0405594v1 fatcat:cj667n2d5rczhonjss5ryv4kue