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The L(n, a, x) function computes the nth generalized Laguerre polynomial with parameter a evaluated at x.
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In the two argument case, L(n, x) computes the nth Laguerre polynomial which is equal to L(n, 0, x).
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The generalized Laguerre polynomials are orthogonal on the interval with respect to the weight function . They satisfy:
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For positive integer a, is related to by:
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Some references define the generalized Laguerre polynomials differently from Maple. Denote the alternate function as . It is defined as:
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For a general positive integer a, the Maple orthopoly[L] function is related to by:
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Laguerre polynomials satisfy the following recurrence relation.
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