Yes, for the factorial-type series we have the Borel-summation, or even the iterated one, as K. Knopp writes it. Knopp distinguishes between Borel's integration-based method and the "simple" method (under the same name Borel).
My problem so far was that I didn't see anywhere a reliable estimate of the coefficients growthrate. so I had to explore this myself, arriving at the guess for a limiting function A(k) as mentioned in my first post in this thread - which of course were a basis for that Borel (or my experimental) method. (I don't remember why, but once in the meantime since I had the impression, the growthrate were more than hypergeometric, and thus Erdös's statement would have made sense. But I couldn't after years not reproduce the reason why I thought so).
I would like to have your (or someone's else) derivation to fix the case for sufficiency Borel-summation for some citeable statement - but as well if even it is only for the better statement in my webspace on tet.-docs... :-)
Hope you've had nice dreams - and read you at sunday -
Gottfried
My problem so far was that I didn't see anywhere a reliable estimate of the coefficients growthrate. so I had to explore this myself, arriving at the guess for a limiting function A(k) as mentioned in my first post in this thread - which of course were a basis for that Borel (or my experimental) method. (I don't remember why, but once in the meantime since I had the impression, the growthrate were more than hypergeometric, and thus Erdös's statement would have made sense. But I couldn't after years not reproduce the reason why I thought so).
I would like to have your (or someone's else) derivation to fix the case for sufficiency Borel-summation for some citeable statement - but as well if even it is only for the better statement in my webspace on tet.-docs... :-)
Hope you've had nice dreams - and read you at sunday -
Gottfried
Gottfried Helms, Kassel
