TASOEV CONTINUED FRACTIONS WITH LONG PERIOD

Takao Komatsu (Japan)

Received August 27, 2007

References:

[1] A. Châtelet, Contribution a la théorie des fractions continues arithmétiques, Bull. Soc. Math. France 40 (1912), 1-25. [2] A. Hurwitz, Über die Kettenbrüche-Entwicklung der Zahl e, Phys.-ökon. Ges. Königsberg 32. Jahrg., 1891 = Mathematische Werke, Band II, Birkhäuser, Basel, 1963, pp. 129-133. [3] A. Hurwitz, Über die Kettenbrüche, deren Teilnenner arithmitische Reihen bilden, Vierteljahrsschrift d. Naturforsch. Gesellschaft in Zürich, Jahrg. 41, 1896 = Mathematische Werke, Band II, Birkhäuser, Basel, 1963, pp. 276-302. [4] T. Komatsu, On Tasoev’s continued fractions, Math. Proc. Cambridge Philos. Soc. 134 (2003), 1-12. [5] T. Komatsu, On Hurwitzian and Tasoev’s continued fractions, Acta Arith. 107 (2003), 161-177. [6] T. Komatsu, Tasoev’s continued fractions and Rogers-Ramanujan continued fractions, J. Number Theory 109 (2004), 27-40. [7] T. Komatsu, Hurwitz and Tasoev continued fractions, Monatsh. Math. 145 (2005), 47-60. [8] T. Komatsu, An algorithm of infinite sums representations and Tasoev continued fractions, Math. Comp. 74 (2005), 2081-2094. [9] T. Komatsu, Hurwitz continued fractions with confluent hypergeometric functions, Czech. Math. J. 57 (2007), 919-932. [10] J. Mc Laughlin and N. J. Wyshinski, Ramanujan and the regular continued fraction expansion of real numbers, Math. Proc. Cambridge Philos. Soc. 138 (2005), 367-381. [11] O. Perron, Die Lehre von den Kettenbrüchen, Band I, Teubner, Stuttgart, 1954. [12] G. N. Raney, On continued fractions and finite automata, Math. Ann. 206 (1973), 265-283. [13] R. F. C. Walters, Alternative derivation of some regular continued fractions, J. Austral. Math. Soc. 8 (1968), 205-212.

Keywords and phrases: Tasoev continued fractions.