Exponential laws for fractional differences
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- by Godfrey L. Isaacs PDF
- Math. Comp. 35 (1980), 933-936 Request permission
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
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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 346352, DOI 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 155121, DOI 10.1112/plms/s3-13.1.430
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 35 (1980), 933-936
- MSC: Primary 39A05
- DOI: https://doi.org/10.1090/S0025-5718-1980-0572866-1
- MathSciNet review: 572866