Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 8 (2013), 59 -- 76## A SPECIAL CASE OF RATIONAL θS FOR TERMINATING θ-EXPANSIONS

## Santanu Chaktaborty

Abstract. 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 [1]. Chakraborty and Rao [3] 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.2010 Mathematics Subject Classification:11J70; 37A45; 37E05.

Keywords:θ-expansions; Generalized Gauss map; Invariant measure.

## References

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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), 49-64. MR1999414. Zbl 1050.60072.C. J. Everett,

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Santanu Chaktaborty

University of Texas-Pan American,

1201 West University, Edinburg, Tx, 78541, USA.

e-mail: schakraborty@utpa.edu