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 , the th fractional difference of . 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 . 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.

**[1]**S. CHAPMAN, "On non-integral orders of summability of series and integrals,"*Proc. London Math. Soc.*(2), v. 9, 1911, pp. 369-409.**[2]**J. B. Díaz and T. J. Osler,*Differences of fractional order*, Math. Comp.**28**(1974), 185–202. MR**0346352**, 10.1090/S0025-5718-1974-0346352-5**[3]**G. L. Isaacs,*An iteration formula for fractional differences*, Proc. London Math. Soc. (3)**13**(1963), 430–460. MR**0155121**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0572866-1

Keywords:
Fractional differences,
successive differences,
exponent law,
summability of series

Article copyright:
© Copyright 1980
American Mathematical Society