I'm trying to research this question and I need links to any of the following papers.
"Baker A (1964) Rational Approximation to certain algebraic numbers. Proc. London Math. Soc 4: 385-308"
"Alladi K and Robinson ML (1980) Legendre polynomials and irrationality. K. Reine Angew. Math 318: 137-155"
I can't find any of them online though.