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Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

Author

Listed:
  • Waritsara Thongthai

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Somsak Orankitjaroen

    (Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand)

  • Chenkuan Li

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

Abstract

In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters ν and γ . We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of ν and γ .

Suggested Citation

  • Waritsara Thongthai & Kamsing Nonlaopon & Somsak Orankitjaroen & Chenkuan Li, 2023. "Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1725-:d:1115769
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    References listed on IDEAS

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    1. Amornrat Sangsuwan & Kamsing Nonlaopon & Somsak Orankitjaroen & Ismail Mirumbe, 2019. "The Generalized Solutions of the n th Order Cauchy–Euler Equation," Mathematics, MDPI, vol. 7(10), pages 1-8, October.
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