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<p>In this article, we explore the analytical foundations of mixed families of special functions through reformulation of umbral formalism, focusing specifically on Legendre-Bessel functions. Our discussion integrates various Bessel-type functions and other family of special polynomials within a cohesive umbral-algebraic framework. This approach gives recent advancements over the formal treatment of higher transcendental functions, facilitating novel and intriguing generalizations. By applying this method to Legendre-Bessel functions, we aim to provide new insights and extend the understanding of these mathematical entities.</p>

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Integral equations for Legendre-Bessel functions through umbral operator

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Maryam Salem Alatawi

摘要

In this article, we explore the analytical foundations of mixed families of special functions through reformulation of umbral formalism, focusing specifically on Legendre-Bessel functions. Our discussion integrates various Bessel-type functions and other family of special polynomials within a cohesive umbral-algebraic framework. This approach gives recent advancements over the formal treatment of higher transcendental functions, facilitating novel and intriguing generalizations. By applying this method to Legendre-Bessel functions, we aim to provide new insights and extend the understanding of these mathematical entities.