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A new pair of multifold inverse series relations will be established with the connection coefficients being expressed in terms of higher derivatives of two fixed multivariate analytic functions, which will be utilized to derive multivariate generalizations of the derivative identities due to Pfaff (1795) and Cauchy (1826), and to review the multiple convolution formulae due to Raney (1960) and Handa-Mohanty (1969/1970).

Multifold inverse series relations and multivariate derivative identities