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On the Rogers--Ramanujan Periodic Continued Fraction.

Authors :
Buslaev, V. I.
Buslaeva, S. F.
Source :
Mathematical Notes; Nov/Dec2003, Vol. 74 Issue 5/6, p783-793, 11p
Publication Year :
2003

Abstract

In the paper, the convergence properties of the Rogers--Ramanujan continued fraction <MATH> 1+\frac{qz}{1+\frac{q^2z}{1+\cdots}} </MATH> are studied for <MATH>q=\exp (2\pi i\tau)</MATH>, where <MATH>\tau</MATH> is a rational number. It is shown that the function <MATH>H_q</MATH> to which the fraction converges is a counterexample to the Stahl conjecture (the hyperelliptic version of the well-known Baker--Gammel--Wills conjecture). It is also shown that, for any rational <MATH>\tau </MATH>, the number of spurious poles of the diagonal Padé approximants of the hyperelliptic function <MATH>H_q</MATH> does not exceed one half of its genus. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00014346
Volume :
74
Issue :
5/6
Database :
Complementary Index
Journal :
Mathematical Notes
Publication Type :
Academic Journal
Accession number :
16822970
Full Text :
https://doi.org/10.1023/B:MATN.0000009014.24386.11