Mobius Sequences

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Published: Apr 19, 2021
Keywords:
Mobius, Sequence

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Sompong Chuysurichay
Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110
Lalita Apisornpanich
Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110

Abstract

In this research, we obtain a new derivation of the closed-form solution of a Mobius sequence defined by


gif.latex?z_{n+1}=\frac{az_n+b}{cz_n+d}


where gif.latex?a,b,c and gif.latex?d are real numbers with gif.latex?ad-bc\neq&space;0

Article Details

How to Cite
Chuysurichay, S., & Apisornpanich, L. (2021). Mobius Sequences. Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 66(703), 32–41. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/217776
Issue
Vol. 66 No. 703 (2021): January - April 2021
Section
Research Article

References

De Pree, J. D. and Thron, W. J. (1962). On Sequences of Moebius Transformations. Mathematische Zeitschrift, 80 (1), p. 184 - 193.

Eljoseph, N. (1968). On The Iteration of Linear Fractional Transformations. The American Mathematical Monthly, 75 (4), p. 362 - 366.

Karlsson, J., Wallin, H., and Gelfgren, J. (1991). Iteration of Möbius Transforms and Continued Fractions. The Rocky Mountain Journal of Mathematics, 21 (1), p. 451 - 472.

Liebeck, H . (1961). The Convergence of Sequences with Linear Fractional Recurrence Relation. The American Mathematical Monthly, 68 (4), p. 353 - 355.

Piranian, G. and Thron, W. J. (1957). Convergence Properties of Sequences of Linear Fractional Transformations. The Michigan Mathematical Journal, 4 (2), p. 129

- 135.