Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Exponential laws for fractional differences

Author: Godfrey L. Isaacs
Journal: Math. Comp. 35 (1980), 933-936
MSC: Primary 39A05
MathSciNet review: 572866
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In Math. Comp., v. 28, 1974, pp. 185-202, Diaz and Osler gave the following (formal) definition for $ {\dot \Delta ^\alpha }f(z)$, the $ \alpha $th fractional difference of $ f(z):{\dot \Delta ^\alpha }f(z) = \Sigma _{p = 0}^\infty A_p^{ - \alpha - 1}f(z + \alpha - p)$. They 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 $ {\Delta ^\alpha }f(z) = \Sigma _{p = 0}^\infty A_p^{ - \alpha - 1}f(z + p)$. In this paper an exponent law for their differences is established and a relation found between the two differences mentioned above. Applications of these results are given.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 39A05

Retrieve articles in all journals with MSC: 39A05

Additional Information

Keywords: Fractional differences, successive differences, exponent law, summability of series
Article copyright: © Copyright 1980 American Mathematical Society