Evaluation of some integrals involving classical polynomials of Hermite and Legendre using Laplace transform method and hypergeometric approach.

• M. I. Qureshi Department of Applied Sciences and Humanities Faculty of Engineering and Technology Central University Jamia Millia Islamia, New Delhi-110025
• Saima Jabee
• M Shadab Department of Applied Sciences and Humanities Faculty of Engineering and Technology Central University Jamia Millia Islamia, New Delhi-110025.

Palabras clave: Teorema de la sumas de Gauss, polinomios clásicos de Legendre de primera clase, polinomios clásicos de Hermite, función hipergeométrica generalizada, Transformada de Laplace

Resumen

En este artículo hemos descrito algunas integrales novedosas asociadas con diferentes polinomios de orden superior, tales como los polinomios clásicos de Hermite y los polinomios clásicos de Legendre. Las siguientes integrales
\begin{equation*}
{\int_{-\infty}^{+\infty}{x^{n}}{\exp(-x^2)}{{H_{n-2k}(x)}}}dx~,
{\int_{-\infty}^{+\infty}{x^{k}}{\exp(-x^2)}{{H_{n}(x)}}}dx~,
\end{equation*}
\begin{equation*}
{\int_{0}^{\infty}{t^{n}}{\exp(-t^2)}{{H_{n}(xt)}}}dt ~~\text{ y }~
{\int_{x}^{\infty}{t^{n+1}}{\exp(-t^2)}{{P_{n}\left(\frac{x}{t}\right)}}}dt
\end{equation*}
Las siguientes integrales se evalúan utilizando el enfoque hipergeométrico y la técnica de transformada de Laplace, que es un enfoque diferente de los enfoques dados por los otros autores en el campo de funciones especiales.

Citas

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