A differential equation for the Rogers-Ramanujan continued fraction

2011 ◽  
pp. 137-144
Keyword(s):  
Differential Equation ◽  
Continued Fraction

scholarly journals On the Continued Fractions associated with the Hypergeometric Equation

1915 ◽  
Vol 34 ◽  
pp. 146-154 ◽  
Author(s):  
E. Lindsay Ince
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Continued Fractions ◽  
Present Author ◽  
Continued Fraction ◽  
Second Order ◽  
Hypergeometric Equation ◽  
Hypergeometric Type ◽  
Linear Differential

The present paper is based on a method attributed to Euler of expressing as a continued fraction the logarithmic derivate of a solu tion of a linear differential equation of the second order. The method is particularly applicable to equations of hypergeometric type, and, in that connection, was previously employed by the present author as a means of adding to the number of known transformations of continued fractions.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

Fuzzy Euler differential equation

2015 ◽  
Vol 2 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. Melliani ◽  
◽  
L. Chadli ◽  
A. Harir
Keyword(s):  
Differential Equation
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