×

On reciprocal sums of terms of linear recurrences. (English) Zbl 0776.11032

The authors prove an irrationality result for the sum of the infinite series whose terms are reciprocals of a recurrent generated sequence of order \(k\), greater than one and two results for the case \(k=2\). Other related results were proved recently by the reviewer [Acta Arith. 63, 313-323 (1993; Zbl 0770.11036)] and by W. L. McDaniel in a paper to appear in Fibonacci Q.
Reviewer: C.Badea (Orsay)

MSC:

11J72 Irrationality; linear independence over a field
11B37 Recurrences

Citations:

Zbl 0770.11036
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] ANDRE-JEANIN R.: A note of the irrationality of certain Lucas infinite series. Fibonacci Quart. 29 (1991), 132-136.
[2] BADEA C.: The irrationality of certain infinite series. Glasgow Math. J. 29 (1987), 221-228. · Zbl 0629.10027
[3] BUNDSCHUH P., PETHÖ A.: Zur Transzendenz gewisser Reihen. Monatsh. Math. 104 (1987), 199-223. · Zbl 0601.10025
[4] ERDÖS P., GRAHAM R. L.: Old and new problems and results in combinatorial number theory. Monograph. Enseign. Math. 38, Enseignement Math., Geneva, 1980, pp. 60-66. · Zbl 0434.10001
[5] GOOD I. J.: A reciprocal series of Fibonacci numbers. Fibonacci Quart. 12 (1974), 346. · Zbl 0292.10009
[6] HOGGATT V. E., BICKNELL M. J.: A reciprocal series of Fibonacci numbers with subscripts of 2nk. Fibonacci Quart 14 (1976), 453-455. · Zbl 0356.10005
[7] OPPENHEIM A.: Criteria for irrationality of certain classes of numbers. Amer. Math. Monthly 61 (1954), 235-241. · Zbl 0055.04503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.