TY - JOUR
T1 - Algebraic relations for reciprocal sums of even terms in Fibonacci numbers
AU - Elsner, Carsten
AU - Shimomura, Shun
AU - Shiokawa, Iekata
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/2
Y1 - 2012/2
N2 - In this paper, we discuss the algebraic independence and algebraic relations, first, for reciprocal sums of even terms in Fibonacci numbers, and second, for sums of evenly even and unevenly even types. The numbers, and are shown to be algebraically independent, and each sum is written as an explicit rational function of these three numbers over ℚ. Similar results are obtained for various series of even type, including the reciprocal sums of Lucas numbers, and.
AB - In this paper, we discuss the algebraic independence and algebraic relations, first, for reciprocal sums of even terms in Fibonacci numbers, and second, for sums of evenly even and unevenly even types. The numbers, and are shown to be algebraically independent, and each sum is written as an explicit rational function of these three numbers over ℚ. Similar results are obtained for various series of even type, including the reciprocal sums of Lucas numbers, and.
UR - http://www.scopus.com/inward/record.url?scp=84855830738&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84855830738&partnerID=8YFLogxK
U2 - 10.1007/s10958-012-0663-0
DO - 10.1007/s10958-012-0663-0
M3 - Article
AN - SCOPUS:84855830738
SN - 1072-3374
VL - 180
SP - 650
EP - 671
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 5
ER -