Korean J. Math. Vol. 27 No. 2 (2019) pp.417-423
DOI: https://doi.org/10.11568/kjm.2019.27.2.417

Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials

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Published: Jun 30, 2019
Keywords:
simplifying, coefficient, ordinary differential equation, generating function, Mittag--Leffler polynomial, Fa\`a di Bruno formula, Bell polynomial of the second kind, Lah inversion formula
Mathematics Subject Classification:
05A15, 11A25, 11B73, 11B83, 11C08, 33E12, 34A05, 42C10.

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Feng Qi
College of Mathematics, Inner Mongolia University for Nationalities Tongliao 028043, Inner Mongolia, China

Abstract

In the paper, by virtue of the Fa\`a di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials.


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