| Title:
|
Hurwitz continued fractions with confluent hypergeometric functions (English) |
| Author:
|
Komatsu, Takao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
919-932 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hurwitz continued fractions |
| MSC:
|
11A55 |
| MSC:
|
11J70 |
| MSC:
|
33C10 |
| idZBL:
|
Zbl 1163.11009 |
| idMR:
|
MR2356930 |
| . |
| Date available:
|
2009-09-24T11:50:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128216 |
| . |
| Reference:
|
[1] A. Châtelet: Contribution a la théorie des fractions continues arithmétiques.Bull. Soc. Math. France 40 (1912), 1–25. MR 1504676 |
| Reference:
|
[2] A. Hurwitz: Über die Kettenbrüche, deren Teilnenner arithmetische Reihen bilden. Vierteljahrsschrift d. Naturforsch. Gesellschaft in Zürich, Jahrg. 41, 1896.. |
| Reference:
|
[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 0595864 |
| Reference:
|
[4] T. Komatsu: On Hurwitzian and Tasoev’s continued fractions.Acta Arith. 107 (2003), 161–177. Zbl 1026.11012, MR 1970821, 10.4064/aa107-2-4 |
| Reference:
|
[5] T. Komatsu: Simple continued fraction expansions of some values of certain hypergeometric functions.Tsukuba J. Math. 27 (2003), 161–173. Zbl 1045.11006, MR 1999242, 10.21099/tkbjm/1496164567 |
| Reference:
|
[6] T. Komatsu: Hurwitz and Tasoev continued fractions.Monatsh. Math. 145 (2005), 47–60. Zbl 1095.11008, MR 2134479, 10.1007/s00605-004-0281-0 |
| Reference:
|
[7] O. Perron: Die Lehre von den Kettenbrüchen, Band I.Teubner, Stuttgart, 1954. Zbl 0056.05901, MR 0064172 |
| Reference:
|
[8] G. N. Raney: On continued fractions and finite automata.Math. Ann. 206 (1973), 265–283. Zbl 0251.10024, MR 0340166, 10.1007/BF01355980 |
| Reference:
|
[9] L. J. Slater: Generalized hypergeometric functions.Cambridge Univ. Press, Cambridge, 1966. Zbl 0135.28101, MR 0201688 |
| Reference:
|
[10] H. S. Wall: Analytic Theory of Continued Fractions.D. van Nostrand Company, Toronto, 1948. Zbl 0035.03601, MR 0025596 |
| . |
