A New Matrix Inversion for Bell Polynomials and Its Applications
Received:July 11, 2018  Revised:April 11, 2019
Key Word: Bell polynomials   Bell matrix   matrix inversion   Lagrange inversion formula   binomial-type sequence   Wronski determinant   Fa\`{a} di Bruno formula  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11401237).
Author NameAffiliation
Jin WANG Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, P. R. China
Department of Mathematics, Soochow University, Jiangsu 215006, P. R. China 
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      The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed form and an inverse form of the classical Fa\`{a} di Bruno formula.
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