1Emeritus Professor, University of Technology Sydney, NSW 2007, Australia, Fellow, Warrane College, University of New South Wales, Kensington NSW 2033
2Department of Mathematics, Faculty of Science & Letters, Kafkas University, 36100, Kars, Turkey
Turkish Journal of Analysis and Number Theory.
2018,
Vol. 6 No. 3, 90-92
DOI: 10.12691/tjant-6-3-4
Copyright © 2018 Science and Education PublishingCite this paper: Anthony G. Shannon, Ömür Deveci. Ward’s Generalized Special Functions.
Turkish Journal of Analysis and Number Theory. 2018; 6(3):90-92. doi: 10.12691/tjant-6-3-4.
Correspondence to: Anthony G. Shannon, Emeritus Professor, University of Technology Sydney, NSW 2007, Australia, Fellow, Warrane College, University of New South Wales, Kensington NSW 2033. Email:
tshannon38@gmail.comAbstract
This paper considers generalizations of Bernoulli and Euler numbers to clarify and extend some known relations studied by Morgan Ward. It does this with the Euler-Maclaurin sum formula. It relates the mappings to category theory as a means of applying the ideas further.
Keywords
Special function,
Bernoulli polynomial,
Euler function,
difference operator,
normal sequence,
divisibility sequence,
difference operator,
generalized integer,
Fermatian numbers,
Euler-Maclaurin sum-formula,
commutative diagram,
category