Realization of a Method for Calculating Bell Polynomials Based on Compositae of Generating Functions

Vadim S. Melman, Yuriy V. Shablya, Dmitry V. Kruchinin, Alexander A. Shelupanov


In this paper different computational methods for calculating partial and n-th complete Bell polynomials are considered. As one of the new methods, the authors propose to use the method for calculating Bell polynomials, which is based on compositae of generating functions. This method was realized by the authors in the form of a library for Wolfram Mathematica and compared with the built-in methods of Wolfram Mathematica and Maple. The results of the comparison demonstrate the advantage of the realization of the new method over the existing ones in spending time and memory for calculating.


Bell polynomial; Calculation; Generating function; Composition; Composita; Library, Wolfram Mathematica

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