An integral analogue of Taylor's series and its use in computing Fourier transforms

Author:
Thomas J. Osler

Journal:
Math. Comp. **26** (1972), 449-460

MSC:
Primary 44A15; Secondary 26A33, 65A05

DOI:
https://doi.org/10.1090/S0025-5718-1972-0306828-1

MathSciNet review:
0306828

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, an integral analogue of Taylor's series

**[1]**A. Erdélyi et al.,*Tables of Integral Transforms*. Vols. I, II, McGraw-Hill, New York, 1954. MR**15**, 868; MR**16**, 468. MR**0061695 (15:868a)****[2]**G. H. Hardy, ``Riemann's form of Taylor's series,''*J. London Math. Soc*., v. 20, 1945, pp. 48-57. MR**8**, 65. MR**0016771 (8:65g)****[3]**T. J. Osler, ``Leibniz rule for fractional derivatives generalized and an application to infinite series,''*SIAM J. Appl. Math.*, v. 18, 1970, pp. 658-674. MR**41**#5562. MR**0260942 (41:5562)****[4]**T. J. Osler, ``The fractional derivative of a composite function,''*SIAM J. Math. Anal.*, v. 1, 1970, pp. 288-293. MR**41**#5563. MR**0260943 (41:5563)****[5]**T. J. Osler, ``Taylor's series generalized for fractional derivatives and applications,''*SIAM J. Math. Anal.*, v. 2, 1971, pp. 37-48. MR**0294612 (45:3682)****[6]**T. J. Osler, ``Fractional derivatives and Leibniz rule,''*Amer. Math. Monthly*, v. 78, 1971, pp. 645-649. MR**1536368****[7]**T. J. Osler, ``A further extension of Leibniz rule to fractional derivatives and its relation to Parseval's formula,''*SIAM J. Math. Anal.*, v. 3, 1972. MR**0323970 (48:2323a)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0306828-1

Keywords:
Fractional derivative,
Fourier integral theorem,
Fourier transforms,
Taylor series,
Lagrange expansion,
special functions

Article copyright:
© Copyright 1972
American Mathematical Society