Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 43 - 1924  

Research Article

On the Relation between Inverse Factorial Series and Binomial Coefficient Series*

W. L. Ferrar

The chief aim of this note is to investigate directly the relation between the inverse factorial series

S0013091500036361_eqn1

and the binomial coefficient series, or Newton's interpolation formula,

S0013091500036361_eqn2

which may also represent Ω(x), the sum of the series (1).

(Received June 05 1924)

Footnotes

* Added August 10th, 1925.—Science Progress for July 1925 notes a paper by J. Horn, “Math. Zeitschrift” 21 (1924) 85.95, in whioh work on differential and difference equations, previously done with inverse factorial series, is carried out with binomial coefficient series. I have been unable to consult the paper itself to see what points in the connection between the two types of series are exemplified.