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Connection Formulae Between Generalized Lucas Polynomials and Some Jacobi Polynomials: Application to Certain Types of Fourth-Order BVPs

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Abstract

In this work, we give new explicit solutions for the connection problems between generalized Lucas polynomial sequence and the two polynomials, namely third and fourth kinds of Chebyshev polynomials. The inversion connection formulae for these formulae are also provided. We show that all the derived expressions involve hypergeometric functions of the type \(_2F_{1}\) of certain arguments. These expressions can be reduced in some specific cases. Based on the derived connection formulae, and as special cases, new connection formulae between first kind Chebyshev, Lucas, Pell–Lucas, Fermat–Lucas, first kind Dickson polynomials and third and fourth kinds of Chebyshev polynomials are deduced. As an application to some of the derived formulae, we give a numerical algorithm for solving certain types of fourth-order boundary value problems based on the application of a modified tau method.

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Acknowledgements

The authors would like to thank the editor for his cooperation and the referee for his constructive and useful comments which have improved the manuscript in its present form.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    W. M. Abd-Elhameed & Y. H. Youssri

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  1. W. M. Abd-Elhameed
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  2. Y. H. Youssri
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Correspondence to Y. H. Youssri.

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Abd-Elhameed, W.M., Youssri, Y.H. Connection Formulae Between Generalized Lucas Polynomials and Some Jacobi Polynomials: Application to Certain Types of Fourth-Order BVPs. Int. J. Appl. Comput. Math 6, 45 (2020). https://doi.org/10.1007/s40819-020-0799-4

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  • DOI: https://doi.org/10.1007/s40819-020-0799-4

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