G-continued fractions for basic hypergeometric functions II

In this paper we apply a modification of a generalized Pringsheim's theorem to obtain a G-continued fraction expansion for the quotient of two contiguous basic hypergeometric functions in arbitrarily many variables. As an application we obtain a G-continued fraction extension of the Rogers–Rama...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 284; číslo 2; s. 435 - 446
Hlavní autoři:	Bowman, Douglas, Choi, Geumlan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	San Diego, CA Elsevier Inc 15.08.2003 Elsevier
Témata:	Algebra Exact sciences and technology Functions of a complex variable Mathematical analysis Mathematics Number theory Sciences and techniques of general use Sequences, series, summability Special functions Fully regular system Recurrence relation Rogers Ramanujan continued fraction Hypergeometric function Convergent series Infinite system Special function Regular system Continued fractions Equation system
ISSN:	0022-247X, 1096-0813
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Abstract	In this paper we apply a modification of a generalized Pringsheim's theorem to obtain a G-continued fraction expansion for the quotient of two contiguous basic hypergeometric functions in arbitrarily many variables. As an application we obtain a G-continued fraction extension of the Rogers–Ramanujan continued fraction.
AbstractList	In this paper we apply a modification of a generalized Pringsheim's theorem to obtain a G-continued fraction expansion for the quotient of two contiguous basic hypergeometric functions in arbitrarily many variables. As an application we obtain a G-continued fraction extension of the Rogers–Ramanujan continued fraction.
Author	Bowman, Douglas Choi, Geumlan
Author_xml	– sequence: 1 givenname: Douglas surname: Bowman fullname: Bowman, Douglas email: bowman@math.uiuc.edu organization: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA – sequence: 2 givenname: Geumlan surname: Choi fullname: Choi, Geumlan email: g-choi1@math.uiuc.edu organization: Mathematics Department, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA
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Cites_doi	10.1090/S0002-9939-1995-1277090-8 10.1006/jmaa.1999.6674 10.1090/conm/166/01624 10.1016/0377-0427(89)90078-2 10.1007/BF02420027
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Keywords	Fully regular system Recurrence relation Rogers Ramanujan continued fraction Hypergeometric function Convergent series Infinite system Special function Regular system Continued fractions Equation system
Language	English
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References	Andrews, Bowman (BIB001) 1995; 123 Bowman, Choi (BIB004) 2000; 243 Thomae (BIB013) 1870; 4 Ramanujan (BIB012) 1962 D. Bowman, J. Sohn, Partial difference equations for basic hypergeometric functions and their Berndt (BIB003) 1991 Pincherle (BIB011) 1894; 32 Lorentzen, Waadeland (BIB010) 1992 continued fractions, J. Reine Angew. Math., under revision Kantorovich, Krylov (BIB006) 1958 Rogers (BIB009) 1894; 25 R.V.M. Zahar, Computational algorithms for linear difference equations, Thesis, Purdue University (1968) Bowman (BIB002) 1994; 166 Levrie, Piessens (BIB008) 1988 Levrie (BIB007) 1989; 25 Kantorovich (10.1016/S0022-247X(02)00521-8_BIB006) 1958 Thomae (10.1016/S0022-247X(02)00521-8_BIB013) 1870; 4 Bowman (10.1016/S0022-247X(02)00521-8_BIB002) 1994; 166 Pincherle (10.1016/S0022-247X(02)00521-8_BIB011) 1894; 32 Levrie (10.1016/S0022-247X(02)00521-8_BIB008) 1988 Bowman (10.1016/S0022-247X(02)00521-8_BIB004) 2000; 243 Rogers (10.1016/S0022-247X(02)00521-8_BIB009) 1894; 25 Andrews (10.1016/S0022-247X(02)00521-8_BIB001) 1995; 123 Ramanujan (10.1016/S0022-247X(02)00521-8_BIB012) 1962 Berndt (10.1016/S0022-247X(02)00521-8_BIB003) 1991 Levrie (10.1016/S0022-247X(02)00521-8_BIB007) 1989; 25 Lorentzen (10.1016/S0022-247X(02)00521-8_BIB010) 1992 10.1016/S0022-247X(02)00521-8_BIB005 10.1016/S0022-247X(02)00521-8_BIB014
References_xml	– volume: 32 start-page: 209 year: 1894 end-page: 291 ident: BIB011 article-title: Delle funzioni ipergeometriche e di varie questioni ad esse attinenti publication-title: Giorn. Mat. Battaglini – volume: 25 start-page: 93 year: 1989 end-page: 104 ident: BIB007 article-title: Pringsheim's theorem revisited publication-title: J. Comput. Appl. Math. – reference: R.V.M. Zahar, Computational algorithms for linear difference equations, Thesis, Purdue University (1968) – volume: 25 start-page: 318 year: 1894 end-page: 343 ident: BIB009 article-title: Second expansion on the expansion of some infinite products publication-title: Proc. London Math. Soc. – year: 1991 ident: BIB003 publication-title: Ramanujan's Notebooks Part III – reference: D. Bowman, J. Sohn, Partial – reference: -continued fractions, J. Reine Angew. Math., under revision – volume: 4 start-page: 105 year: 1870 end-page: 138 ident: BIB013 article-title: Les séries Heinéennes supérieures, ou les éries de la forme publication-title: Ann. Mat. Pura Appl. – start-page: 349 year: 1988 end-page: 370 ident: BIB008 article-title: Convergence accelerations for Miller's algorithm publication-title: Nonlinear Numerical Methods and Rational Approximation – year: 1958 ident: BIB006 publication-title: Approximate Methods of Higher Analysis – year: 1992 ident: BIB010 publication-title: Continued Fractions with Applications – volume: 123 start-page: 3343 year: 1995 end-page: 3350 ident: BIB001 article-title: A full extension of the Rogers–Ramanujan continued fraction publication-title: Proc. Amer. Math. Soc. – volume: 166 start-page: 155 year: 1994 end-page: 165 ident: BIB002 article-title: Modified convergence for publication-title: Contemp. Math. – reference: -difference equations for basic hypergeometric functions and their – volume: 243 start-page: 338 year: 2000 end-page: 343 ident: BIB004 publication-title: J. Math. Anal. Appl. – year: 1962 ident: BIB012 publication-title: Collected Papers – start-page: 349 year: 1988 ident: 10.1016/S0022-247X(02)00521-8_BIB008 article-title: Convergence accelerations for Miller's algorithm – volume: 123 start-page: 3343 year: 1995 ident: 10.1016/S0022-247X(02)00521-8_BIB001 article-title: A full extension of the Rogers–Ramanujan continued fraction publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1995-1277090-8 – year: 1992 ident: 10.1016/S0022-247X(02)00521-8_BIB010 – volume: 243 start-page: 338 year: 2000 ident: 10.1016/S0022-247X(02)00521-8_BIB004 article-title: G-continued fractions for basic hypergeometric functions publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1999.6674 – year: 1962 ident: 10.1016/S0022-247X(02)00521-8_BIB012 – ident: 10.1016/S0022-247X(02)00521-8_BIB014 – volume: 32 start-page: 209 year: 1894 ident: 10.1016/S0022-247X(02)00521-8_BIB011 article-title: Delle funzioni ipergeometriche e di varie questioni ad esse attinenti publication-title: Giorn. Mat. Battaglini – volume: 166 start-page: 155 year: 1994 ident: 10.1016/S0022-247X(02)00521-8_BIB002 article-title: Modified convergence for q-continued fraction defined by functional relations publication-title: Contemp. Math. doi: 10.1090/conm/166/01624 – year: 1958 ident: 10.1016/S0022-247X(02)00521-8_BIB006 – volume: 25 start-page: 318 year: 1894 ident: 10.1016/S0022-247X(02)00521-8_BIB009 article-title: Second expansion on the expansion of some infinite products publication-title: Proc. London Math. Soc. – volume: 25 start-page: 93 year: 1989 ident: 10.1016/S0022-247X(02)00521-8_BIB007 article-title: Pringsheim's theorem revisited publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(89)90078-2 – ident: 10.1016/S0022-247X(02)00521-8_BIB005 – volume: 4 start-page: 105 year: 1870 ident: 10.1016/S0022-247X(02)00521-8_BIB013 article-title: Les séries Heinéennes supérieures, ou les éries de la forme 1+∑n=0∞xn1−qa1−q1−qa+11−q2⋯1−qa+n−11−qn1−qa′1−qb′1−qa′+11−qb′+1⋯1−qa′+n−11−qb′+n−1⋯1−qa(h)1−qb(h)1−qa(h)+11−qb(h)+1⋯1−qa(h)+n−11−qb(h)+n−1 publication-title: Ann. Mat. Pura Appl. doi: 10.1007/BF02420027 – year: 1991 ident: 10.1016/S0022-247X(02)00521-8_BIB003
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Title	G-continued fractions for basic hypergeometric functions II
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