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July 1, 2026Mathematical Methods in the Applied Sciences0 citations

Complete Asymptotic Expansions of Operators Related to Generalized Laguerre and Touchard Polynomials

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VGVijay GuptaPurdue University West LafayetteVSV. D. SharmaNetaji Subhas University of Technology

Key Points

  • This research aims to develop complete asymptotic expansions for operators linked to generalized Laguerre and Touchard polynomials.
  • Derived asymptotic expansions for linear positive operators associated with generalized Laguerre and Touchard polynomials.
  • Established difference estimates using moduli of smoothness to improve approximation accuracy.
  • Used graphical illustrations to assess rates of convergence.
  • Provided specific methods that improve the order of approximation by these operators.
  • Established quantitative difference estimates showing significant performance of operators.
  • Illustrated convergence rates graphically, highlighting the effectiveness of the methods employed.

Abstract

ABSTRACT In this article, we provide complete asymptotic expansions of the linear positive operators associated with the generalized Laguerre and Touchard polynomials, respectively. We also provide specific methods to obtain better order of approximation by these operators. Moreover, we establish quantitative difference estimates for these operators with respect to their components through moduli of smoothness. Finally, we investigate their rates of convergence through graphical illustrations.

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Cite This Study

Gupta et al. (2026) studied this question.

synapsesocial.com/papers/6a44ae315cd2549c8bc43790https://doi.org/10.1002/mma.70862
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