scholarly journals On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 638
Author(s):  
Pavel Trojovský
Keyword(s):  
Higher Order ◽  
Order Linear ◽  
Recursive Sequence ◽  
Infinite Sums ◽  
Reciprocal Sums

Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, including a reciprocal of polynomial applied to linear higher order recurrences.

scholarly journals On the Higher Power Sums of Reciprocal Higher-Order Sequences

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhengang Wu ◽  
Jin Zhang
Keyword(s):  
Error Estimation ◽  
Higher Order ◽  
Analytic Method ◽  
Order Linear ◽  
Power Sums ◽  
Higher Power ◽  
Recursive Sequence ◽  
Finite Sums ◽  
Reciprocal Sums

Let{un}be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher-order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.

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