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orthopoly[L] - Laguerre polynomial
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Calling Sequence
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L(n, a, x)
L(n, x)
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Parameters
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n
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non-negative integer
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a
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rational number greater than -1 or nonrational algebraic expression
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x
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algebraic expression
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Description
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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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![L(n, a, x) = (-1)^a*(diff(L(a+n, x), [`$`(x, a)]))](/support/helpjp/helpview.aspx?si=7046/file04398/math115.png)
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Some references define the generalized Laguerre polynomials differently from Maple. Denote the alternate function as  . It is defined as:
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![altL(n, a, x) = diff(altL(n, x), [`$`(x, a)])](/support/helpjp/helpview.aspx?si=7046/file04398/math124.png)
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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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Examples
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Using the alternate definition for the Laguerre polynomials:
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 end proc](/support/helpjp/helpview.aspx?si=7046/file04398/math201.png)
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