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Multiple Derivative Inversions and Lagrange-Good Expansion Formulae

Author

Listed:
  • Wenchang Chu

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
    Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

Abstract

By establishing new multiple inverse series relations (with their connection coefficients being given by higher derivatives of fixed multivariate analytic functions), we illustrate a general framework to provide new proofs for MacMahon’s master theorem and the multivariate expansion formula due to Good (1960). Further multivariate extensions of the derivative identities due to Pfaff (1795) and Cauchy (1826) will be derived and the generalized multifold convolution identities due to Carlitz (1977) will be reviewed.

Suggested Citation

  • Wenchang Chu, 2022. "Multiple Derivative Inversions and Lagrange-Good Expansion Formulae," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4234-:d:971127
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