\begin{equation*} \int_{-a}^{a}e^{-\rho x}P_n \left( \frac{x}{a} \right) dx = (-1)^n\sqrt{\frac{2\pi a}{\rho}}J_{n+1/2}(a\rho) ~~~~~~\text{for $a>0$} \end{equation*}
I am just wondering this formula is correct or not? Thanks in advance!
2026-03-27 18:07:52.1774634872
Definite Integral in Legendre polynomial formula
131 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in BESSEL-FUNCTIONS
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