Convergence of Newton series What is the condition for a real valued function of a real variable to have a Newton series which converges to that function pointwise? 
It feels like there should be a condition similar to that for the Taylor series.

I have been pointed recently that convergence of Newton series is covered extensively in Gelfond, A. O. Calculus of finite differences. Translated from the Russian. International Monographs on Advanced Mathematics and Physics. Hindustan Publishing Corp., Delhi, 1971
The Russian original is available online:
http://inis.jinr.ru/sl/vol1/UH/_Ready/Mathematics/Gel%27fond%20A.%20Ischislenie%20konechnyh%20raznostej%20%281959%29%28ru%29%28L%29%28201s%29.pdf
Page 141 onwards.
