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Summation of certain infinite Lucas-related series
[article]

2019
*
arXiv
*
pre-print

In this paper, we find the sums in closed form

arXiv:1901.04336v1
fatcat:p4oxh2p4jnemropxzho3r7bjxi
*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*. ...##
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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. ...##
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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. ...##
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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 ...##
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Page 5376 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
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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. ...##
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Reflex mechanisms and the physiology of nerve and muscle

1918
*
Psychological bulletin
*

Another paper by

doi:10.1037/h0072724
fatcat:dl5wwecxmbclhbixogfbpldtgm
*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. ...##
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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. ...##
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Periodicities in the Theory of Partitions

1922
*
Annals of Mathematics
*

This is in sharp contrast to the usual analysis in which all

doi:10.2307/1967762
fatcat:ndppkr5u5zbotbp267bghtpdmq
*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. ...##
###
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. ...##
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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. ...

##
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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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