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Expansions by means of the Fractional Calculus
Published online by Cambridge University Press: 03 November 2016
Extract
We have shown how the theory of the Fractional Calculus enables us to expand functions in various forms. In the present paper we shall obtain some further expansions.
A λth integral of f(z) along a simple curve l is defined by
where γ is the least integer greater than or equal to zero such that R(λ) + γ>0, D stands for d/dz, and the integration and differentiation are along l.
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- Copyright © Mathematical Association 1937
References
page no 396 note * Fabian, , Phil. Mag. (7) 20 (1935), 781-9CrossRefGoogle Scholar. Quarterly Journ. of Math. (1936).
page no 396 note † Fabian, , Phil. Mag. (7) 20 (1935), 781-9CrossRefGoogle Scholar.
page no 396 note ‡ f-λ-n(z 0) stands for Dλ+n(la)f(z0), and, generally, fλ(z will be written for D-λ (la)f(z), when no ambiguity can arise.
page no 396 note § Fabian, Quarterly Journ. of Math. (1936).
page no 397 note * Fabian, , Phil. Mag. (7) 20 (1935), 781-9CrossRefGoogle Scholar.
page no 398 note * Fabian, , Phil. Mag. (7) 20 (1935), 781-9CrossRefGoogle Scholar.