A special case of rational θs for terminating θ-expansions
There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A class of random continued fractions with singula...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2013-12-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v08/p06.pdf |
| _version_ | 1818113437355474944 |
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| author | Santanu Chaktaborty |
| author_facet | Santanu Chaktaborty |
| author_sort | Santanu Chaktaborty |
| collection | DOAJ |
| description | There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A class of random continued fractions with singular equillibria, Perspectives in Statistical Science. eds A.K.Basu et al, Oxford University Press, 2000]. Chakraborty and Rao [θ-expansions and the generalized Gauss map, Probability, Statistics and their Applications: Papers in Honor of Rabi Bhattacharya. eds Athreya, K. et al, IMS Lect. Notes, Monogr. Ser. 41 (2003)] subsequently did elaborate studies on θ-expansions in their paper. They also obtained the unique invariant measure for the Markov process associated with the generalized Gauss transformation that generated θ-expansions for some special θs. In this work, we investigate an interesting question regarding the nature of θs for θ-expansion of 1/θ terminating at stage two, particularly with θ rational. |
| first_indexed | 2024-12-11T03:34:49Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-12-11T03:34:49Z |
| publishDate | 2013-12-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-c7c3b95eae6849a8a58fa6b140c0a8c82022-12-22T01:22:16ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982013-12-018 (2013)5976A special case of rational θs for terminating θ-expansionsSantanu Chaktaborty0University of Texas-Pan American, 1201 West University, Edinburg, Tx, 78541, USAThere have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A class of random continued fractions with singular equillibria, Perspectives in Statistical Science. eds A.K.Basu et al, Oxford University Press, 2000]. Chakraborty and Rao [θ-expansions and the generalized Gauss map, Probability, Statistics and their Applications: Papers in Honor of Rabi Bhattacharya. eds Athreya, K. et al, IMS Lect. Notes, Monogr. Ser. 41 (2003)] subsequently did elaborate studies on θ-expansions in their paper. They also obtained the unique invariant measure for the Markov process associated with the generalized Gauss transformation that generated θ-expansions for some special θs. In this work, we investigate an interesting question regarding the nature of θs for θ-expansion of 1/θ terminating at stage two, particularly with θ rational.http://www.utgjiu.ro/math/sma/v08/p06.pdfθ-expansionsGeneralized Gauss mapInvariant measure |
| spellingShingle | Santanu Chaktaborty A special case of rational θs for terminating θ-expansions Surveys in Mathematics and its Applications θ-expansions Generalized Gauss map Invariant measure |
| title | A special case of rational θs for terminating θ-expansions |
| title_full | A special case of rational θs for terminating θ-expansions |
| title_fullStr | A special case of rational θs for terminating θ-expansions |
| title_full_unstemmed | A special case of rational θs for terminating θ-expansions |
| title_short | A special case of rational θs for terminating θ-expansions |
| title_sort | special case of rational θs for terminating θ expansions |
| topic | θ-expansions Generalized Gauss map Invariant measure |
| url | http://www.utgjiu.ro/math/sma/v08/p06.pdf |
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