Results 21 to 30 of about 15,160 (203)
AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS
Journal of Science Natural ScienceWe report on an integral representation for the Pell sequence, Pell-Lucas sequence, Balancing sequence and Lucas-Balancing sequence. This integral representation is based on the generating function and the Binet-like formulas of the aforementioned ...
Nguyen Duc Sang, Luu Ba Thang
core +3 more sources
Reciprocal Formulae among Pell and Lucas Polynomials
Mathematics, 2022 Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions.
Mei Bai, Wenchang Chu, Dongwei Guo
exaly +4 more sources
On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers
Axioms, 2023 Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico +2 more
doaj +3 more sources
Some properties of bicomplex Pell and Pell-Lucas numbers
Journal of Information and Optimization Sciences, 2021 In this work, we investigated bicomplex Pell and Pell-Lucas numbers.
Serpil Halici +3 more
core +4 more sources
On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers [PDF]
Mathematica Pannonica, 2023 Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in ...
Kouessi Norbert Ad'edji +1 more
semanticscholar +4 more sources
ON SUMS OF SQUARES OF PELL-LUCAS NUMBERS
Integers, 2006 In this paper we prove several formulas for sums of squares of even Pell-Lucas numbers, sums of squares of odd Pell-Lucas numbers, and sums of products of even and odd Pell-Lucas numbers.
Gianella, Gian Mario +3 more
core +5 more sources
Effect of Bacille Calmette-Guérin vaccination on immune responses to SARS-CoV-2 and COVID-19 vaccination. [PDF]
Clin Transl ImmunologyBacille Calmette–Guérin (BCG), the vaccine for tuberculosis, has immunomodulatory effects that may underpin its off‐target effects on infectious disease risk and vaccine responses. This study used blood samples taken before and 28 days after COVID‐19 vaccinations (2‐dose primary course), from healthcare workers randomised to receive BCG vaccine or no ...
Messina NL +23 more
europepmc +2 more sources
On generalized (k, r)-Pell and (k, r)-Pell–Lucas numbers
Bulletin of the Malaysian Mathematical Sciences Society, 2022 We introduce new kinds of k-Pell and k-Pell–Lucas numbers related to the distance between numbers by a recurrence relation and show their relation to the (k,r)-Pell and (k,r)-Pell–Lucas numbers.
Bahar Kuloǧlu, E. Özkan
semanticscholar +3 more sources
A NOTE ON BIGAUSSIAN PELL AND PELL-LUCAS NUMBERS
Journal of Science and Arts, 2021 In this study, we define a new type of Pell and Pell-Lucas numbers which are called biGaussian Pell and biGaussian Pell-Lucas numbers. We also give the relationship between negabiGaussian Pell and Pell-Lucas numbers and bicomplex Pell and Pell-Lucas ...
Hasan Gökbaş
semanticscholar +2 more sources
A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)
Communications in Mathematics and Applications, 2019 In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as \begin{align*} Q_{n}= \begin{cases} 2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even ...
Sukran Uygun, H. Karataş
semanticscholar +3 more sources