(11/14/2009, 10:05 PM)bo198214 Wrote: I am skeptical about those Borel-summation. Usually it requires the summable function to be of at most exponential type (or perhaps even fixed nested exponential type).

Perhaps, but could it be used to sum the diverging coefficients of the Faulhaber applied to the Taylor series, though (which would have a slower growth), instead of the series itself (which describes the fast growing tetrational)?

Yet I still am wondering why it seems so tough to get it going for their example function.

Though regardless, I'm still curious about that Mittag-Leffler expansion thing. Anything on how to determine those magic constants? Do you have access to the references mentioned?