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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Shrnutí: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(02)00521-8