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...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000517 |
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| _version_ | 1832556022040887296 |
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| author | Geoffrey B. Campbell |
| author_facet | Geoffrey B. Campbell |
| author_sort | Geoffrey B. Campbell |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-d427f5e1278d4834b884262650215d43 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d427f5e1278d4834b884262650215d432025-02-03T05:46:32ZengWileyInternational 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. |
| 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. |
| title | 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_short | A generalized formula of Hardy |
| title_sort | generalized formula of hardy |
| 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 |