Laguerre functions: tables and properties

Abstract

The first 21 Laguerre functions have been tabulated to four decimal places (or two significant figures when this is more accurate) for values of the argument 0(0-l)l(0-2)3(0-5)6(l)14(2)40(5)100. The practical applications of these functions are briefly considered. The zeros of these Laguerre functions are also tabulated to 5 places, the last of which is not reliable except in the case of the smallest zero for orders above 6. Differentiation and integration of Laguerre functions, orthonormal properties and addition formulae are briefly discussed. Finite or infinite series of Laguerre functions whose sums are well-known functions such as products of polynomials and circular or exponential functions, step and delta functions, Bessel and Kelvin functions, and gamma and error functions are stated. The general methods used for deriving some of these results are indicated in Section 13.