Roots of Legendre Polynomial I was wondering if the following properties of the Legendre polynomials are true in general. They hold for the first ten or fifteen polynomials.


*

*Are the roots always simple (i.e., multiplicity $1$)?

*Except for low-degree cases, the roots can't be calculated exactly, only approximated (unlike Chebyshev polynomials).

*Are roots of the entire family of Legendre Polynomials dense in the interval $[0,1]$ (i.e., it's not possible to find a subinterval, no matter how small, that doesn't contain at least one root of one polynomial)?
If anyone knows of an article/text that proves any of the above, please let me know.  The definition of these polynomials can be found on Wikipedia.

The Abramowitz–Stegun Handbook of Mathematical Functions claims on page 787 that all the roots are simple: http://convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150&Page=787
