Hurwitz continued fractions with confluent hypergeometric functions

Takao Komatsu

Czechoslovak Mathematical Journal (2007)

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

Abstract

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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 0 F 1 ( ; c ; z ) . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.

How to cite

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Komatsu, 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

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  2. Über die Kettenbrüche, deren Teilnenner arithmetische Reihen bilden. Vierteljahrsschrift d.  Naturforsch. Gesellschaft in Zürich, Jahrg.  41, 1896, . 
  3. Continued Fractions: Analytic Theory and Applications (Encyclopedia of mathematics and its applications, Vol.  11), Addison-Wesley, Reading, 1980. (1980) MR0595864
  4. 10.4064/aa107-2-4, Acta Arith. 107 (2003), 161–177. (2003) Zbl1026.11012MR1970821DOI10.4064/aa107-2-4
  5. Simple continued fraction expansions of some values of certain hypergeometric functions, Tsukuba J.  Math. 27 (2003), 161–173. (2003) Zbl1045.11006MR1999242
  6. 10.1007/s00605-004-0281-0, Monatsh. Math. 145 (2005), 47–60. (2005) Zbl1095.11008MR2134479DOI10.1007/s00605-004-0281-0
  7. Die Lehre von den Kettenbrüchen, Band  I, Teubner, Stuttgart, 1954. (1954) Zbl0056.05901MR0064172
  8. 10.1007/BF01355980, Math. Ann. 206 (1973), 265–283. (1973) Zbl0251.10024MR0340166DOI10.1007/BF01355980
  9. Generalized hypergeometric functions, Cambridge Univ. Press, Cambridge, 1966. (1966) Zbl0135.28101MR0201688
  10. Analytic Theory of Continued Fractions, D.  van Nostrand Company, Toronto, 1948. (1948) Zbl0035.03601MR0025596

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