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A bug in Laguerre-L?

asked 2014-10-21 16:54:59 -0500

Peter Luschny gravatar image

updated 2014-10-22 06:02:02 -0500

laguerre(-1,1) returns 0 in Sage but returns exp(1) in Maple and Mathematica.

The docs say: "Return the Laguerre polynomial for integers n>−1."

Is this expected behaviour to return an innocent value instead of giving the user a warning?

Edit: I give an example how this behaviour can bite: Look at the Inverse Lah transform of 1,2,3,... which starts 1, -2, -1, 2, 17, 94, 487, ... This can be computed by

factorial(n)*(laguerre(n,1)-2*laguerre(n-1,1))

This expression gives for n=0 the expected value '1' and thus hides the fact that the formula is true only for n>0!

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answered 2014-10-21 19:23:28 -0500

kcrisman gravatar image

Great point. Those orthogonal polynomials haven't had much TLC for a long time. I've opened http://trac.sagemath.org/ticket/17192 for this.

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Asked: 2014-10-21 16:54:59 -0500

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Last updated: Oct 22 '14