# Hurwitz continued fractions with confluent hypergeometric functions

Czechoslovak Mathematical Journal (2007)

- Volume: 57, Issue: 3, page 919-932
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topKomatsu, Takao. "Hurwitz continued fractions with confluent hypergeometric functions." Czechoslovak Mathematical Journal 57.3 (2007): 919-932. <http://eudml.org/doc/31172>.

@article{Komatsu2007,

abstract = {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.},

author = {Komatsu, Takao},

journal = {Czechoslovak Mathematical Journal},

keywords = {Hurwitz continued fractions; confluent hypergeometric function},

language = {eng},

number = {3},

pages = {919-932},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Hurwitz continued fractions with confluent hypergeometric functions},

url = {http://eudml.org/doc/31172},

volume = {57},

year = {2007},

}

TY - JOUR

AU - Komatsu, Takao

TI - Hurwitz continued fractions with confluent hypergeometric functions

JO - Czechoslovak Mathematical Journal

PY - 2007

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 57

IS - 3

SP - 919

EP - 932

AB - 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.

LA - eng

KW - Hurwitz continued fractions; confluent hypergeometric function

UR - http://eudml.org/doc/31172

ER -

## References

top- Contribution a la théorie des fractions continues arithmétiques, Bull. Soc. Math. France 40 (1912), 1–25. (1912) MR1504676
- Über die Kettenbrüche, deren Teilnenner arithmetische Reihen bilden. Vierteljahrsschrift d. Naturforsch. Gesellschaft in Zürich, Jahrg. 41, 1896, .
- Continued Fractions: Analytic Theory and Applications (Encyclopedia of mathematics and its applications, Vol. 11), Addison-Wesley, Reading, 1980. (1980) MR0595864
- 10.4064/aa107-2-4, Acta Arith. 107 (2003), 161–177. (2003) Zbl1026.11012MR1970821DOI10.4064/aa107-2-4
- Simple continued fraction expansions of some values of certain hypergeometric functions, Tsukuba J. Math. 27 (2003), 161–173. (2003) Zbl1045.11006MR1999242
- 10.1007/s00605-004-0281-0, Monatsh. Math. 145 (2005), 47–60. (2005) Zbl1095.11008MR2134479DOI10.1007/s00605-004-0281-0
- Die Lehre von den Kettenbrüchen, Band I, Teubner, Stuttgart, 1954. (1954) Zbl0056.05901MR0064172
- 10.1007/BF01355980, Math. Ann. 206 (1973), 265–283. (1973) Zbl0251.10024MR0340166DOI10.1007/BF01355980
- Generalized hypergeometric functions, Cambridge Univ. Press, Cambridge, 1966. (1966) Zbl0135.28101MR0201688
- Analytic Theory of Continued Fractions, D. van Nostrand Company, Toronto, 1948. (1948) Zbl0035.03601MR0025596

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.