This statement seems to imply that the series would converge, but we just said that it diverges. Provide a secondary reference discussing this with some context. Also, the fine structure constant is larger than 10^-3, and alpha^2 > 10^-5, so how does it follow that second order approximation in alpha is good to 10^-10? (en)
Not sure if this hypothesis is needed, why this is not in Sakurai ? (en)
