scholarly journals Convolution of second order linear recursive sequences II.

2017 ◽  
Vol 25 (2) ◽  
pp. 137-148
Author(s):  
Tamás Szakács
Keyword(s):  
Second Order ◽  
Characteristic Polynomials ◽  
Common Root ◽  
Order Linear ◽  
Recursive Sequences

Abstract We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

On the approximation of quadratic algebraic numbers

2005 ◽  
Vol 42 (2) ◽  
pp. 195-205
Author(s):  
Sándor H.-Molnár
Keyword(s):  
Positive Integer ◽  
Algebraic Number ◽  
Algebraic Integer ◽  
Second Order ◽  
Algebraic Numbers ◽  
Order Linear ◽  
Recursive Sequences ◽  
Approximating Sequence ◽  
Real Quadratic

In the paper we construct such second order linear recursive sequences G and H of rational integers that with their terms |a -Gn+1 /H n| < 1/ (\sqrtvDH2n) holds for every positive integer n, where a denotes a real quadratic algebraic integer of discriminant D. An approximating sequence of the form Gn+1 /Hn is also given for a  if it is only a real quadratic algebraic number (not an algebraic integer), but in this case the approximating constant is not the best.

Bases for Second Order Linear ODEs

2020 ◽  
Vol 127 (9) ◽  
pp. 849-849
Author(s):  
Peter McGrath
Keyword(s):  
Second Order ◽  
Order Linear ◽  
Linear Odes

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

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