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inlineconstexpr |
Computes the value of the Laguerre and associated Laguerre polynomials of order n
at x
:
Defined in header
Parameters
n
, m
: integral positive arguments.x
: real floating argument.Return value
The value of the polynomial at x
is returned.
The expression successor(laguerre)(n, x, ln, lnm1)
implements the three term recurrence relation for the Laguerre polynomials, \(\displaystyle \mbox{L}_{n+1} =
\left((2n+1-x)\mbox{L}_{n}-n\mbox{L}_{n-1}\right)/(n+1)\)
The expression successor(laguerre)(n, m, x, ln, lnmm1)
implements the three term recurrence relation for the associated Laguerre polynomials, \(\displaystyle \mbox{L}_{n+1}^m =
\left((m+2n+1-x)\mbox{L}_{n}^{m}-(m+n)\mbox{L}_{n-1}^{m}\right)/(n+1)\)
These functions can be used to create a sequence of values evaluated at the same x
(and m
) and for rising n
.
Example