Differential equations associated with generalized Bell polynomials and their zeros

Abstract

Abstract:In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials. We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.

Differential Equations Arising from the 3-Variable Hermite Polynomials and Computation of Their Zeros

“…Hence, by (19) and (20), and comparing the coefficients of Here is a plot of the surface for this solution. In Figure 1(left), we choose À2 ≤ z ≤ 2, À1 ≤ t ≤ 1, x ¼ 2, and y ¼À4.…”

“…Recently, many mathematicians have studied the differential equations arising from the generating functions of special polynomials (see [7,8,12,[16][17][18][19]). In this paper, we study differential equations arising from the generating functions of the 3-variable Hermite polynomials.…”

Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations

“…Recently, many mathematicians have studied the differential equations arising from the generating functions of special polynomials (see [4][5][6][7][8]). Inspired by their work, we give a differential equations by generation of (r, β)-Bell polynomials G n (x, r, β) as follows.…”

Nonlinear differential equations associated with degenerate tangent numbers

“…The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of differential equations often encountered in physical problems. Very recently, many mathematicians have studied in the area of the Euler numbers, Bernoulli numbers, tangent numbers, degenerate Euler numbers, degenerate Bernoulli numbers, and degenerate tangent numbers(see [1,2,3,6,7,8,9,10]). In [1], L. Carlitz introduced the degenerate Bernoulli polynomials.…”

“…Many mathematicians have studied in the area of the linear and nonlinear differential equations arising from the generating functions of special polynomials in order to give explicit identities for special polynomials(see [2,8,9]). In this paper, we study nonlinear differential equations arising from the generating functions of degenerate tangent numbers.…”