scholarly journals Algebraic independence of modified reciprocal sums of products of Fibonacci numbers

2006 ◽  
Vol 30 (2) ◽  
pp. 345-361
Author(s):  
Taka-aki Tanaka
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence ◽  
Sums Of Products ◽  
Reciprocal Sums

scholarly journals On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 178
Author(s):  
Younseok Choo
Keyword(s):  
Recurrence Relation ◽  
Fibonacci Numbers ◽  
Sums Of Products ◽  
Reciprocal Sums

This paper concerns the properties of the generalized bi-periodic Fibonacci numbers {Gn} generated from the recurrence relation: Gn=aGn−1+Gn−2 (n is even) or Gn=bGn−1+Gn−2 (n is odd). We derive general identities for the reciprocal sums of products of two generalized bi-periodic Fibonacci numbers. More precisely, we obtain formulas for the integer parts of the numbers ∑k=n∞(a/b)ξ(k+1)GkGk+m−1,m=0,2,4,⋯, and ∑k=n∞1GkGk+m−1,m=1,3,5,⋯.

Algebraic independence results for reciprocal sums of Fibonacci numbers

2011 ◽  
Vol 148 (3) ◽  
pp. 205-223 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence ◽  
Independence Results ◽  
Reciprocal Sums

scholarly journals Algebraic relations for reciprocal sums of Fibonacci numbers

2007 ◽  
Vol 130 (1) ◽  
pp. 37-60 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Reciprocal Sums

scholarly journals Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers

1997 ◽  
Vol 73 (7) ◽  
pp. 140-142 ◽  
Author(s):  
Daniel Duverney ◽  
Keiji Nishioka ◽  
Kumiko Nishioka ◽  
Iekata Shiokawa
Keyword(s):  
Continued Fraction ◽  
Fibonacci Numbers ◽  
Reciprocal Sums

Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers

2007 ◽  
Vol 17 (3) ◽  
pp. 429-446 ◽  
Author(s):  
C. Elsner ◽  
S. Shimomura ◽  
I. Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Reciprocal Sums

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.

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