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Taylor’s Series Generalized for Fractional Derivatives and Applications

- T. Osler
- Mathematics
- 1 February 1971

The familiar Taylor’s series expansion of the function , $f(z)$ has for its general term $D^n f(z_0 ){{(z - z_0 )^n } / {n!}}$. A new generalization of Taylor’s series in which the general term is… Expand

Leibniz Rule for Fractional Derivatives Generalized and an Application to Infinite Series

- T. Osler
- Mathematics
- 1 May 1970

Differences of fractional order

- J. B. Díaz, T. Osler
- Mathematics
- 1974

Derivatives of fractional order, D af, have been considered extensively in the literature. However, little attention seems to have been given to finite differences of frac- tional order, A af. In… Expand

Fundamental properties of fractional derivatives via pochhammer integrals

- J. Lavoie, R. Tremblay, T. Osler
- Mathematics
- 1975

In this paper, various representations of fractional differentiation are explored, and a definition using Pochhammer contour integrals emerges as deserving special emphasis. The analyticity of… Expand

Fractional Derivatives and Special Functions

- J. L. Lovoie, T. Osler, R. Tremblay
- Mathematics
- 1 April 1976

The fractional derivative operator is an extension of the familiar derivative operator $D^n $ to arbitrary (integer, rational, irrational, or complex) values of n. The most important representation...

The Integral Analog of the Leibniz Rule

- T. Osler
- Mathematics
- 13 January 1972

This paper demonstrates that the classical Leibniz rule for the derivative of the product of two functions

A Child's Garden of Fractional Derivatives

- Maria Kleinz, T. Osler
- Mathematics
- 1 March 2000

Tom Osler (osler@rowan.edu) is a professor of mathematics at Rowan University. He received his Ph.D. from the Courant Institute at New York University in 1970 and is the author of twenty-three… Expand

The Union of Vieta's and Wallis's Products for Pi

- T. Osler
- Mathematics
- 1 October 1999

While (1) and (2) seem unrelated, they are both special cases of a more general double product (3). The first product in (3) consists of the first p factors of Vieta's original infinite product (1).… Expand

A Further Extension of the Leibniz Rule to Fractional Derivatives and Its Relation to Parseval’s Formula

- T. Osler
- Mathematics
- 1 February 1972

The familiar Leibniz rule for the Nth derivative of the product of two functions is $D^N uv = \sum {\left( {\begin{array}{*{20}c} N \\ n \\ \end{array} } \right)D^{N - n} uD^n v}$. A generalization… Expand

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