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ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 56, Issue 1, pp 77–89 | Cite as

On a continued fraction of order six

  • K. R. Vasuki
  • N. Bhaskar
  • G. Sharath
Article

Abstract

In this paper, we derive certain identities for the following continued of order six:

$$ X(q)\,:=\,q^{1/4} \frac{\sum\nolimits_{n=0}^\infty\frac{(-q;q^2)_nq^{n^2+2n}}{(q^4;q^4)_n}}{\sum\nolimits_{n=0}^{\infty} \frac{q^{n^2}}{(q^2;q^2)_n}} $$
$$ =\,\frac{q^{-1/4}(1-q^2)}{(1-q^{3/2})} _+\frac{(1-q^{1/2})(1-q^{7/2})}{q^{1/2}(1-q^{3/2})(1+q^3)} _+\frac{(1-q^{5/2})(1-q^{13/2})}{q^{3/2}(1-q^{3/2})(1+q^6 )}_{+\ldots}. $$

Keywords

Continued fraction Theta functions 

Mathematics Subject Classification (2000)

11A55 33D10 

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Copyright information

© Università degli Studi di Ferrara 2010

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreManasagangotri, MysoreIndia
  2. 2.Department of MathematicsVidyavardhaka College of EngineeringGokulum, MysoreIndia

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