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Summation of certain infinite Lucas-related series [article]

Bakir Farhi
2019 arXiv   pre-print
In this paper, we find the sums in closed form of certain type of Lucas-related convergent series.  ...  More precisely, we generalize the results already obtained by the author in his arXiv paper entitled: "Summation of certain infinite Fibonacci related series".  ...  We investigate two types of infinite Lucas-related series.  ... 
arXiv:1901.04336v1 fatcat:p4oxh2p4jnemropxzho3r7bjxi

Page 2484 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
F. (5-NENG) Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence-generated sequences. Fibonacci Quart. 26 (1988), no. 2, 98-114.  ...  Bergum associated Fermat’s solution with certain terms of the Fibonacci sequence and on this basis were able to obtain infinitely many solutions of the problem.  ... 

Page 5278 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
(TN-TUNISS-E) Lambert series and the summation of reciprocals in certain Fibonacci-Lucas-type sequences. Fibonacci Quart. 28 (1990), no. 3, 223-226.  ...  Let 4:,42,°:: be an infinite sequence of integers greater than one and A be any real number.  ... 

Page 9 of Mathematical Reviews Vol. , Issue 88b [page]

1988 Mathematical Reviews  
In much of the paper, the authors evaluate a number of infinite series involving reciprocals of products of Pell and Pell-Lucas numbers.  ...  F. (5-NENG) Infinite series summation involving reciprocals of Pell polynomials. Fibonacci numbers and their applications (Patras, 1984), 163-180, Math.  ... 

Page 89 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Rotkiewicz, There are 2000a: 1 1027 infinitely many arithmetical progressions formed by three differ- ent Fibonacci pseudoprimes (327-332); Ken-Ichi Sato [Ken-ichi Sato'], On Mikolas’ summation formula  ...  Howard and Richard Witt, Lacunary sums of binomial coefficients (185-195); Derek Jennings, Some reciprocal summation identities with applications to the Fibonacci and Lucas numbers (197-200); Clark Kimberling  ... 

Page 5376 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
with a set L of infinite Christoffel words and the action of homographies of PGL,(Z) on P! with the action of certain substitutions on L.  ...  relation.  ... 

Page 5134 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
Pentti Haukkanen (SF-TAM; Tampere) 95i:11013 11B39 Zhang, Zhi Zheng Some summation formula of generalized Fibonacci, Lucas sequence. (English summary) Pure Appl. Math. 10 (1994), suppl., 209-212.  ...  (2) A is an asymp- totic basis of order 2 of all infinite elements T; of 7, then A is called an asymptotic pseudo-basis of N*.  ... 

Page 262 of Mathematical Reviews Vol. 39, Issue 2 [page]

1970 Mathematical Reviews  
Brousseau, Brother Alfred 1389 Summation of infinite Fibonacci series. Fibonacci Quart. 7 (1969), 143-168. Duncan, R. L. 1390 On the density of the k-free integers.  ...  The nth Lucas quaternion 7’, is similarly defined, F,, being replaced by the nth Lucas number JL,. The author gives lists of relations involving Q,, 7',, F, and L,. James, R.  ... 

Reflex mechanisms and the physiology of nerve and muscle

Edwin. B. Holt
1918 Psychological bulletin  
Another paper by Lucas (14) deals with summation in the claw mechanism of Astacus.  ...  The posthumous book of Keith Lucas (13) , in Starling's Monograph series, has been arranged for the press by E. D. Adrian from manuscript left by the author.  ... 
doi:10.1037/h0072724 fatcat:dl5wwecxmbclhbixogfbpldtgm

Page 1177 of Mathematical Reviews Vol. 51, Issue 4 [page]

1976 Mathematical Reviews  
These are applied to the integration of rational functions, the summation of certain infinite series, interpolation by expo- nential sums, and combinatorial analysis. Corresponding to a  ...  M. 8377 A description of invariant measures for actions of certain infinite- dimensional groups. (Russian) Dokl. Akad. Nauk SSSR 218 (1974), 749-752.  ... 

Periodicities in the Theory of Partitions

E. T. Bell
1922 Annals of Mathematics  
This is in sharp contrast to the usual analysis in which all relations between denumerants and functions of a continuous parameter involve infinite series or products.  ...  Relations with Lucas' Functions. Thus far p, q are arbitrary real quantities. When p, q are integers, the it, v in all of the above relations are Lucas' functions.  ... 
doi:10.2307/1967762 fatcat:ndppkr5u5zbotbp267bghtpdmq

Page 6082 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
=9, ds = 69,--- is a certain integer sequence.  ...  T= So TU (TH. = j- The summation is over all nonnegative integral values of k, to k,, such that j =k, +---+ jk;. Several interesting corollaries of (*) are deduced including the results of A.  ... 

Page 679 of Mathematical Reviews Vol. 32, Issue 4 [page]

1966 Mathematical Reviews  
Lehner and the reviewer to prove that 1 _ 12 log 2 kk(k+k’) where k, k’ run over all consecutive. pairs of denominators in the Farey series of order n.  ...  The author establishes a number of identities involving sums of Fibonacci numbers, all obtained by summation by parts. R. J. Levit (San Francisco, Calif.) 4073 Horadam, A.  ... 

Page 2112 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
Summation of reciprocal series of a class of polynomials. (English and Macedonian summaries) Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi 15 (1994), no. 2, 33-36 (1996).  ...  The author considers the polynomials of Fibonacci, Lucas, Pell and Lucas-Pell, F,, L,, Pn, Q, respectively.  ... 

Page 78 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
Denef, Multiplic- ity of the poles of the Poincaré series of a p-adic subanalytic set (Exp. No. 43, 8 pp.); Shunji Ito, On Legendre’s theorem related to Diophantine approximations (Exp.  ...  .); Jean Cougnard, Résultats récents sur la monogénéité de certains anneaux d’entiers [Recent results on the monogeneity of certain rings of integers] (Exp.  ... 
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