Geodesic
Hurwitz continued fractions with confluent hypergeometric functions
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 919-932

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions ${}_0F_1(;c;z)$. In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.
Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions ${}_0F_1(;c;z)$. In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.
Classification : 11A55, 11J70, 33C10
Keywords: Hurwitz continued fractions 
Komatsu, Takao. Hurwitz continued fractions with confluent hypergeometric functions. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 919-932. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a10/
@article{CMJ_2007_57_3_a10,
     author = {Komatsu, Takao},
     title = {Hurwitz continued fractions with confluent hypergeometric functions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {919--932},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356930},
     zbl = {1163.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a10/}
}
TY  - JOUR
AU  - Komatsu, Takao
TI  - Hurwitz continued fractions with confluent hypergeometric functions
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 919
EP  - 932
VL  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a10/
LA  - en
ID  - CMJ_2007_57_3_a10
ER  - 
%0 Journal Article
%A Komatsu, Takao
%T Hurwitz continued fractions with confluent hypergeometric functions
%J Czechoslovak Mathematical Journal
%D 2007
%P 919-932
%V 57
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a10/
%G en
%F CMJ_2007_57_3_a10

[1] A. Châtelet: Contribution a la théorie des fractions continues arithmétiques. Bull. Soc. Math. France 40 (1912), 1–25. | MR

[2] A.  Hurwitz: Über die Kettenbrüche, deren Teilnenner arithmetische Reihen bilden. Vierteljahrsschrift d.  Naturforsch. Gesellschaft in Zürich, Jahrg.  41, 1896.

[3] W. B.  Jones, W. J.  Thron: Continued Fractions: Analytic Theory and Applications (Encyclopedia of mathematics and its applications, Vol.  11). Addison-Wesley, Reading, 1980. | MR

[4] T.  Komatsu: On Hurwitzian and Tasoev’s continued fractions. Acta Arith. 107 (2003), 161–177. | DOI | MR | Zbl

[5] T.  Komatsu: Simple continued fraction expansions of some values of certain hypergeometric functions. Tsukuba J.  Math. 27 (2003), 161–173. | DOI | MR | Zbl

[6] T.  Komatsu: Hurwitz and Tasoev continued fractions. Monatsh. Math. 145 (2005), 47–60. | DOI | MR | Zbl

[7] O.  Perron: Die Lehre von den Kettenbrüchen, Band  I. Teubner, Stuttgart, 1954. | MR | Zbl

[8] G. N.  Raney: On continued fractions and finite automata. Math. Ann. 206 (1973), 265–283. | DOI | MR | Zbl

[9] L. J.  Slater: Generalized hypergeometric functions. Cambridge Univ. Press, Cambridge, 1966. | MR | Zbl

[10] H. S.  Wall: Analytic Theory of Continued Fractions. D.  van Nostrand Company, Toronto, 1948. | MR | Zbl