Sign issue in special values of Legendre Polynomials

[Dan Cross]

Hi,

It seems the special values of the Legendre Polynomials evaluated at zero are hard coded to be positive, but the sign should alternate.  So, while legendre_P(0,0) correctly gives 1 and legendre_P(4,0) correctly gives 3/8, legendre_P(2,0) gives +1/2 instead of -1/2.  Evaluating legendre_P(2,x) for any x close to zero gives a value close to -1/2 as it should.  This problem is even evident on the documentation page (https://paulmasson.github.io/sagemath-docs/functions/legendre_P.html) which shows the graph of P_2 passing through -1/2 but tabulates the special value at zero as +1/2.

Thanks.

[Vincent Delecroix]

There is indeed a problem

sage: legendre_P(2, 0)
1/2
sage: legendre_P(2.0, 0.0)
-0.500000000000000

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[dmo...@deductivepress.ca]

Thanks for reporting the bug. I opened trac ticket #33962 to fix it.