Exponential laws for fractional differences
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.
-  S. CHAPMAN, "On non-integral orders of summability of series and integrals," Proc. London Math. Soc. (2), v. 9, 1911, pp. 369-409.
-  J. B. Díaz and T. J. Osler, Differences of fractional order, Math. Comp. 28 (1974), 185–202. MR 0346352, https://doi.org/10.1090/S0025-5718-1974-0346352-5
-  G. L. Isaacs, An iteration formula for fractional differences, Proc. London Math. Soc. (3) 13 (1963), 430–460. MR 0155121, https://doi.org/10.1112/plms/s3-13.1.430
- S. CHAPMAN, "On non-integral orders of summability of series and integrals," Proc. London Math. Soc. (2), v. 9, 1911, pp. 369-409.
- J. B. DIAZ & T. J. OSLER, "Differences of fractional order," Math. Comp., v. 28, 1974, pp. 185-202. MR 0346352 (49:11077)
- G. L. ISAACS, "An iteration formula for fractional differences," Proc. London Math. Soc. (3), v. 13, 1963, pp. 430-460. MR 0155121 (27:5061)
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Keywords: Fractional differences, successive differences, exponent law, summability of series
Article copyright: © Copyright 1980 American Mathematical Society