Title

The Fractional Calculus And Its Role In The Synthesis Of Special Functions: Part Ii

Abstract

This paper is concerned with applications of the arbitrary order derivintegrals of generalized hypergeometric functions to the synthesis of special functions. It is shown that the whole spectrum of special functions can be expressed in terms of three basic functions including the inverse binomial, the exponential and the Bessel functions of zero order. Several formulae for the arbitrary order derivintegral of the NFD and nGFD hypergeometric functions. A systematic method of evaluation of the derivintegrals of the important transcendental and special functions is developed in this paper. Three tables are included in the paper. Tables 1, 2 and 3 include Dαxderivintegrals ofNGFDhypergeometric functions for N=D, N=D-1, and N=D-2 respectively. A listing of the reducible special functions includes exponential integrals and error functions, logarithms, inverse trigonometric functions, and their hyperbolic counterparts, incomplete γ-and β-functions, circular and hyperbolic sines, cosines, and sine integrals, Bessel functions, generalized special functions such as Gauss, Kummer and other hypergeometric and elliptic integrals. It is shown that the derivintegral operator forges a very powerful link among all the special functions. © 1988 Taylor and Francis Group, LLC.

Publication Date

5-1-1988

Publication Title

International Journal of Mathematical Education in Science and Technology

Volume

19

Issue

3

Number of Pages

347-362

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/0020739880190301

Socpus ID

84946343370 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84946343370

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