Steffensen J.F. Note on Divided Differences

Danske Vid. Selsk. Math.-Fys. Medd. 17 (1939), XXII, 3.The number of general theorems concerning divide differences is so small that any addition to the list may, perhaps, be welcome. The unexpectedly simple theorem which forms the object of this Note seems, as far as I have been able to ascertain, to be new; it may be regarded as a generalization of Leibniz' formula for the r^th derivate of a product of two functions.