Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients

Ronald Orozco López

Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients

Number Theory 2021-05-12 v2 Classical Analysis and ODEs

Authors: Ronald Orozco López

Abstract

In this paper special values of Bell polynomials are given by using the power series solution of the equation $y^{(k)}=e^{ay}$ . In addition, complete and partial exponential autonomous functions, exponential autonomous polynomials, autonomous polynomials and $(k,a)$ -autonomous coefficients are defined. Finally, we show the relationship between various numbers counting combinatorial objects and binomial coefficients, Stirling numbers of the second kind and autonomous coefficients.

Keywords

bell polynomials differential equation autonomous coefficients power series solution stirling numbers combinatorial numbers

Cite

@article{arxiv.2103.13478,
  title  = {Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients},
  author = {Ronald Orozco López},
  journal= {arXiv preprint arXiv:2103.13478},
  year   = {2021}
}

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Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients

Abstract

Keywords

Cite

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