Abstract
We present a symmetrical addition formula for the general Laguerre polynomials $L_n^\alpha (Z)$ with argument $Z = x + y + 2\sqrt {xy} rt - xyr^2 $. The formula involves a finite sum of Laguerre and Hermite polynomials, and can be integrated to give a new product formula for $L_n^\alpha (x)L_n^\alpha (y)$. This addition formula is obtained as a limiting case of Koornwinder’s addition formula for the Jacobi polynomials.
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