Exponential Laws for Fractional Differences

Godfrey L. Isaacs
1980 Mathematics of Computation  
In Math. Comp., v. 28, 1974, pp. 185-202, Diaz and Osier gave the follow 1 ing (formal) definition for kaf(z), the ath fractional difference of f(z): Âa/(z) = -n=o-^p f(z "*■ a ~ P)-T"ey derived formulas and applications involving this difference. They asked whether their differences satisfied an exponent law and what the relation was between their differences and others, such as Aaf(z) -£p_Q.4p /(z + P). In this paper an exponent law for their differences is established and a relation found
more » ... a relation found between the two differences mentioned above. Applications of these results are given.
doi:10.2307/2006204 fatcat:xnn2f6ejlbdt5l22dvi5fgso5a