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Mathematics of Computation
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0572866-1
PII: S 0025-5718(1980)0572866-1
Keywords: Fractional differences, successive differences, exponent law, summability of series
Article copyright: © Copyright 1980 American Mathematical Society