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Certain properties of Konhauser matrix polynomials via Lie Algebra techniques

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Abstract

The principal purpose of this paper is devoted to an investigation of some interesting generating matrix functions for the second-kind Konhauser matrix polynomials (KMPs) using a Lie group theory. We derive many interesting properties such as Rodrigues formula, integral representations, matrix recurrence relations, matrix differential equation, finite sums and generating matrix functions for the second-kind KMPs.

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Acknowledgements

(a) The author expresses sincere appreciation to Dr. Mohamed Saleh Metwally [Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Egypt], and Dr. Mahmoud Tawfik Mohamed [Department of Mathematics, Faculty of Science (New Valley), Assiut University, New Valley, EL-Kharga 72111, Egypt] for their kind interests, encouragement, help, suggestions, comments and the investigations for this series of papers. (b) The author would like to thank the anonymous reviewers for their valuable comments and suggestions, which improve the readability of the paper.

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Correspondence to Ayman Shehata.

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Shehata, A. Certain properties of Konhauser matrix polynomials via Lie Algebra techniques. Bol. Soc. Mat. Mex. 26, 99–120 (2020). https://doi.org/10.1007/s40590-019-00232-8

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Keywords

  • Konhauser matrix polynomials
  • Matrix recurrence relations
  • Matrix differential equations
  • Generating matrix functions
  • Lie group theory

Mathematics Subject Classification

  • Primary 33C25
  • 33C80
  • Secondary 33E20
  • 15A60