Simplifying coefficients in differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials

Feng Qi abstract: In the paper, by virtue of the Faá di Bruno formula and identities for the Bell polynomials of the second kind, the author simplifies coefficients in a family of ordinary differential equations related to generating functions of reverse Bessel and partially degenerate Bell polynomials.

[1]  Feng Qi,et al.  On multivariate logarithmic polynomials and their properties , 2018, Indagationes Mathematicae.

[2]  Feng Qi (祁锋).  Notes on Several Families of Differential Equations Related to the Generating Function for the Bernoulli Numbers of the Second Kind , 2018, Turkish Journal of Analysis and Number Theory.

[3]  Feng Qi (祁锋),et al.  Some properties of the Bernoulli numbers of the second kind and their generating function , 2018 .

[4]  Identities involving Bessel polynomials arising from linear differential equations , 2016, 1602.04106.

[5]  Dongkyu Lim,et al.  Some properties and an application of multivariate exponential polynomials , 2020, Mathematical Methods in the Applied Sciences.

[6]  Feng Qi (祁锋),et al.  The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices , 2017 .

[7]  Feng Qi (祁锋),et al.  Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials , 2017 .

[8]  Feng Qi (祁锋),et al.  Simplifying differential equations concerning degenerate Bernoulli and Euler numbers , 2017 .

[9]  Feng Qi (祁锋),et al.  Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations , 2019 .

[10]  Feng Qi (祁锋),et al.  SOME IDENTITIES AND A MATRIX INVERSE RELATED TO THE CHEBYSHEV POLYNOMIALS OF THE SECOND KIND AND THE CATALAN NUMBERS , 2017 .

[11]  L. Comtet,et al.  Advanced Combinatorics: The Art of Finite and Infinite Expansions , 1974 .

[12]  Feng Qi,et al.  Integral representations for multivariate logarithmic polynomials , 2018, J. Comput. Appl. Math..

[13]  Feng Qi (祁锋).  Some inequalities for the Bell numbers , 2017 .

[14]  Feng Qi (祁锋).  Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Mittag--Leffler polynomials , 2019 .

[15]  Feng Qi (祁锋),et al.  Special values of the Bell polynomials of the second kind for some sequences and functions , 2020, Journal of Mathematical Analysis and Applications.

[16]  Feng Qi (祁锋),et al.  Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations , 2017 .

[17]  Feng Qi (祁锋),et al.  Some Inequalities of the Incomplete Gamma and Related Functions , 1999 .

[18]  Feng Qi (祁锋),et al.  Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials , 2016 .

[19]  Feng Qi,et al.  Monotonicity Results and Inequalities for the Gamma and Incomplete Gamma Functions , 2002 .

[20]  Feng Qi,et al.  Some properties of central Delannoy numbers , 2018, J. Comput. Appl. Math..

[21]  Feng Qi (祁锋),et al.  SEVERAL EXPLICIT AND RECURSIVE FORMULAS FOR THE GENERALIZED MOTZKIN NUMBERS , 2017 .

[22]  Feng Qi (祁锋),et al.  Some Properties of the Hermite Polynomials and Their Squares and Generating Functions , 2016 .

[23]  Feng Qi (祁锋),et al.  Simplifying and finding ordinary differential equations in terms of the stirling numbers , 2018 .

[24]  Feng Qi (祁锋),et al.  INEQUALITIES FOR THE INCOMPLETE GAMMA AND RELATED FUNCTIONS , 1999 .

[25]  Feng Qi (祁锋),et al.  Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers , 2018, Tatra Mountains Mathematical Publications.

[26]  Feng Qi (祁锋),et al.  Several formulas for special values of the Bell polynomials of the second kind and applications , 2017 .

[27]  Feng Qi (祁锋),et al.  The inverse of a triangular matrix and several identities of the Catalan numbers , 2019, Applicable Analysis and Discrete Mathematics.

[28]  Feng Qi (祁锋),et al.  Simplification of Coefficients in Two Families of Nonlinear Ordinary Differential Equations , 2018, Turkish Journal of Analysis and Number Theory.

[29]  Feng Qi (祁锋),et al.  Some identities for a sequence of unnamed polynomials connected with the Bell polynomials , 2019 .

[30]  Feng Qi (祁锋),et al.  Expansions of the exponential and the logarithm of power series and applications , 2017, Arabian Journal of Mathematics.

[31]  Feng Qi (祁锋),et al.  Derivative polynomials of a function related to the Apostol-Euler and Frobenius-Euler numbers , 2017 .

[32]  Some inequalities and an application of exponential polynomials , 2020 .

[33]  Feng Qi (祁锋).  Simplifying coefficients in a family of nonlinear ordinary differential equations , 2019, Acta et commentationes Universitatis Tartuensis de mathematica.

[34]  Feng Qi (祁锋),et al.  Some Properties and Generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers , 2018 .

[35]  Feng Qi,et al.  Diagonal recurrence relations for the Stirling numbers of the first kind , 2013, Contributions Discret. Math..

[36]  Feng Qi (祁锋),et al.  Explicit Expressions Related to Degenerate Cauchy Numbers and Their Generating Function , 2018, Mathematical Modelling, Applied Analysis and Computation.

[37]  Feng Qi (祁锋),et al.  Simplifying coefficients in differential equations for generating function of Catalan numbers , 2019, Journal of Taibah University for Science.

[38]  An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions , 2014, 1402.2361.

[39]  Feng Qi (祁锋).  An Explicit Formula for the Bell Numbers in Terms of the Lah and Stirling Numbers , 2014, 1401.1625.

[40]  Feng Qi (祁锋),et al.  Some identities related to Eulerian polynomials and involving the Stirling numbers , 2018 .

[41]  Feng Qi (祁锋),et al.  Explicit formulas and recurrence relations for higher order Eulerian polynomials , 2017 .