scholarly journals Modular equations for cubes of the Rogers–Ramanujan and Ramanujan–Göllnitz–Gordon functions and their associated continued fractions

2012 ◽  
Vol 132 (7) ◽  
pp. 1519-1553 ◽  
Author(s):  
Chadwick Gugg
Keyword(s):  
Continued Fractions ◽  
Modular Equations ◽  
Associated Continued Fractions

scholarly journals ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

2017 ◽  
Vol 13 (2) ◽  
pp. 7147-7154
Author(s):  
Anthony G Shannon ◽  
Charles K Cook b ◽  
Rebecca A. Hillman c
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Fibonacci Numbers ◽  
Recursive Sequences ◽  
Essential Idea ◽  
Associated Continued Fractions ◽  
Generalized Continued Fractions

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements.

Continued Logarithms and Associated Continued Fractions

2016 ◽  
Vol 26 (4) ◽  
pp. 412-429
Author(s):  
Jonathan M. Borwein ◽  
Neil J. Calkin ◽  
Scott B. Lindstrom ◽  
Andrew Mattingly
Keyword(s):  
Continued Fractions ◽  
Associated Continued Fractions

scholarly journals Some New Explicit Values of Quotients of Theta-Function ϕ(q) and Applications to Ramanujan's Continued Fractions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nipen Saikia
Keyword(s):  
Theta Function ◽  
Continued Fractions ◽  
Modular Equations ◽  
Real Numbers ◽  
Positive Real ◽  
Ramanujan’S Theta Function

We find some new explicit values of the parameter hk,n for positive real numbers k and n involving Ramanujan's theta-function ϕ(q) and give some applications of these new values for the explicit evaluations of Ramanujan's continued fractions. In the process, we also establish two new identities for ϕ(q) by using modular equations.

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