A generalized formula of Hardy

We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi-crystal structure and self-similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power...

Full description

Bibliographic Details
Main Author:	Geoffrey B. Campbell
Format:	Article
Language:	English
Published:	Hindawi Limited 1994-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	combinatorial identities Farey sequences; analytic theory of partitions combinatorial inequalities fractals partitions of integers.
Online Access:	http://dx.doi.org/10.1155/S0161171294000517

id	doaj-d427f5e1278d4834b884262650215d43
record_format	Article
spelling	doaj-d427f5e1278d4834b884262650215d432020-11-24T20:42:58ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117236937810.1155/S0161171294000517A generalized formula of HardyGeoffrey B. Campbell0Institute of Advanced Studies, School of Mathematical Sciences, The Australian National University, GPO Box 4, Canberra 2601, AustraliaWe give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi-crystal structure and self-similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood's High Indices Theorem. Over a decade ago, Mahler and then others proved results on irrationality of decimal fractions applicable to types of functions we consider.http://dx.doi.org/10.1155/S0161171294000517combinatorial identitiesFarey sequences; analytic theory of partitionscombinatorial inequalitiesfractalspartitions of integers.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Geoffrey B. Campbell
spellingShingle	Geoffrey B. Campbell A generalized formula of Hardy International Journal of Mathematics and Mathematical Sciences combinatorial identities Farey sequences; analytic theory of partitions combinatorial inequalities fractals partitions of integers.
author_facet	Geoffrey B. Campbell
author_sort	Geoffrey B. Campbell
title	A generalized formula of Hardy
title_short	A generalized formula of Hardy
title_full	A generalized formula of Hardy
title_fullStr	A generalized formula of Hardy
title_full_unstemmed	A generalized formula of Hardy
title_sort	generalized formula of hardy
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1994-01-01
description	We give new formulae applicable to the theory of partitions. Recent work suggests they also relate to quasi-crystal structure and self-similarity. Other recent work has given continued fractions for the type of functions herein. Hardy originally gave such formulae as ours in early work on gap power series which led to his and Littlewood's High Indices Theorem. Over a decade ago, Mahler and then others proved results on irrationality of decimal fractions applicable to types of functions we consider.
topic	combinatorial identities Farey sequences; analytic theory of partitions combinatorial inequalities fractals partitions of integers.
url	http://dx.doi.org/10.1155/S0161171294000517
work_keys_str_mv	AT geoffreybcampbell ageneralizedformulaofhardy AT geoffreybcampbell generalizedformulaofhardy
_version_	1716821033462267904

A generalized formula of Hardy

Similar Items