In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for...In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.展开更多
We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furth...We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11971341 and 12001492the Natural Science Foundation of Zhejiang Province under Grant No.LQ20A010004.
文摘In this paper,by means of the classical Lagrange inversion formula,the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper[J.Wang,Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula,J.Integer Seq.,Vol.22(2019),Article 19.3.8].As applications of this inverse relation,the authors not only find a short proof of another nonlinear inverse relation due to Birmajer,et al.(2012),but also set up a few convolution identities concerning the Mina polynomials.
基金Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（YT080320, LYI2A01030） Supported by the National Natural Science Foundation of China（l1226297） Supported by the Zhejiang Univerity City College Scientific Research Foundation（J-13003）
文摘We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.
