Two generalizations of Ramanujan's continued fraction identities

1985 ◽  
pp. 56-62 ◽  
Author(s):  
S. Bhargava ◽  
Chandrashekar Adiga
Keyword(s):  
Continued Fraction ◽  
Ramanujan's Continued Fraction

Ramanujan's Continued Fraction and the Bauer-Muir Transformation

1961 ◽  
Vol 57 (1) ◽  
pp. 76-79 ◽  
Author(s):  
V. N. Singh
Keyword(s):  
Positive Integer ◽  
Gamma Function ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Gamma Functions ◽  
Image Position ◽  
The Right ◽  
Basic Analogue ◽  
Ramanujan's Continued Fraction

Ramanujan's Continued Fraction may be stated as follows: Let where there are eight gamma functions in each product and the ambiguous signs are so chosen that the argument of each gamma function contains one of the specified number of minus signs. Then where the products and the sums on the right range over the numbers α, β, γ, δ, ε: provided that one of the numbers β, γ, δ, ε is equal to ± ±n, where n is a positive integer. In 1935, Watson (3) proved the theorem by induction and also gave a basic analogue. In this paper we give a new proof of Ramanujan's Continued Fraction by using the transformation of Bauer and Muir in the theory of continued fractions (Perron (1), §7;(2), §2).

On some generalizations of Ramanujan’s continued fraction identities

1987 ◽  
Vol 97 (1-3) ◽  
pp. 31-43 ◽  
Author(s):  
S. Bhargava ◽  
Chandrashekar Adiga ◽  
D. D. Somashekara
Keyword(s):  
Continued Fraction ◽  
Ramanujan's Continued Fraction

A Combinatorial Interpretation of Ramanujan's Continued Fraction

1968 ◽  
Vol 11 (3) ◽  
pp. 405-408 ◽  
Author(s):  
G. Szekeres
Keyword(s):  
Continued Fraction ◽  
Present Note ◽  
Combinatorial Interpretation ◽  
Image Position ◽  
Positive Integers ◽  
Ramanujan's Continued Fraction

The purpose of the present note is to give a combinatorial interpretation of the coefficients of expansion of the Ramanujan continued fraction ([1], p. 295)The result is expressed by formula (12) below.The enumeration of distinct score vectors of a tournament leads to the following problem: (Erdős and Moser, see Moon [2], p. 68). Given n ≥ 1, k ≥ 0, determine the number of distinct sequences of positive integers

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