scholarly journals On the reciprocal sums of products of Fibonacci and Lucas numbers

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2911-2920 ◽  
Author(s):  
Ginkyu Choi ◽  
Younseok Choo
Keyword(s):  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers ◽  
Sums Of Products ◽  
Reciprocal Sums

In this paper, we study the reciprocal sums of products of Fibonacci and Lucas numbers. Some identities are obtained related to the numbers ??,k=n 1/FkLk+m and ??,k=n 1/LkFk+m, m ? 0.

ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES

2014 ◽  
Vol 98 (3) ◽  
pp. 289-310 ◽  
Author(s):  
PETER BUNDSCHUH ◽  
KEIJO VÄÄNÄNEN
Keyword(s):  
Rational Function ◽  
Complex Number ◽  
Functional Equations ◽  
Algebraic Independence ◽  
Lucas Numbers ◽  
Mahler Functions ◽  
Independence Results ◽  
Nonzero Complex Number ◽  
Fibonacci And Lucas Numbers ◽  
Reciprocal Sums

This paper considers algebraic independence and hypertranscendence of functions satisfying Mahler-type functional equations $af(z^{r})=f(z)+R(z)$, where $a$ is a nonzero complex number, $r$ an integer greater than 1, and $R(z)$ a rational function. Well-known results from the scope of Mahler’s method then imply algebraic independence over the rationals of the values of these functions at algebraic points. As an application, algebraic independence results on reciprocal sums of Fibonacci and Lucas numbers are obtained.

scholarly journals On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 350
Author(s):  
Younseok Choo
Keyword(s):  
Lucas Numbers ◽  
Balancing Numbers ◽  
Sums Of Products ◽  
Reciprocal Sums

Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing numbers and products of balancing and Lucas-balancing numbers. The method of this paper can also be applied to even-indexed and odd-indexed Fibonacci, Lucas, Pell and Pell–Lucas numbers.

scholarly journals Sums of products of generalized Fibonacci and Lucas numbers

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Zvonko Čerin
Keyword(s):  
Recent Work ◽  
Recurrence Relation ◽  
Fixed Number ◽  
Binomial Coefficients ◽  
Natural Numbers ◽  
Lucas Numbers ◽  
Alternating Sums ◽  
Explicit Formulae ◽  
Fibonacci And Lucas Numbers ◽  
Sums Of Products

AbstractIn this paper we obtain explicit formulae for sums of products of a fixed number of consecutive generalized Fibonacci and Lucas numbers. These formulae are related to the recent work of Belbachir and Bencherif. We eliminate all restrictions about the initial values and the form of the recurrence relation. In fact, we consider six different groups of three sums that include alternating sums and sums in which terms are multiplied by binomial coefficients and by natural numbers. The proofs are direct and use the formula for the sum of the geometric series.

Exceptional algebraic relations for reciprocal sums of Fibonacci and Lucas numbers

2011 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa ◽  
Masaaki Amou ◽  
Masanori Katsurada
Keyword(s):  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers ◽  
Reciprocal Sums
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