On Balancing and Lucas-balancing Quaternions

Bijan Kumar Patel; Prasanta Kumar Ray

Communications in Mathematics (2021)

  • Volume: 29, Issue: 3, page 325-341
  • ISSN: 1804-1388

Abstract

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The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.

How to cite

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Patel, Bijan Kumar, and Ray, Prasanta Kumar. "On Balancing and Lucas-balancing Quaternions." Communications in Mathematics 29.3 (2021): 325-341. <http://eudml.org/doc/297538>.

@article{Patel2021,
abstract = {The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.},
author = {Patel, Bijan Kumar, Ray, Prasanta Kumar},
journal = {Communications in Mathematics},
keywords = {Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions},
language = {eng},
number = {3},
pages = {325-341},
publisher = {University of Ostrava},
title = {On Balancing and Lucas-balancing Quaternions},
url = {http://eudml.org/doc/297538},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Patel, Bijan Kumar
AU - Ray, Prasanta Kumar
TI - On Balancing and Lucas-balancing Quaternions
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 325
EP - 341
AB - The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
LA - eng
KW - Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions
UR - http://eudml.org/doc/297538
ER -

References

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  2. Behera, A., Panda, G.K., On the square roots of triangular numbers, Fibonacci Quarterly, 37, 1999, 98-105, THE FIBONACCI ASSOCIATION, (1999) 
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  8. Horadam, A.F., 10.2307/2313129, The American Mathematical Monthly, 70, 3, 1963, 289-291, JSTOR, (1963) DOI10.2307/2313129
  9. Horadam, A.F., Quaternion recurrence relations, Ulam Quarterly, 2, 2, 1993, 23-33, (1993) 
  10. Iyer, M.R., A note on Fibonacci quaternions, Fibonacci Quarterly, 7, 3, 1969, 225-229, (1969) 
  11. Panda, G.K., Ray, P.K., Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 6, 1, 2011, 41-72, Citeseer, (2011) MR2850087
  12. Ray, P.K., Curious congruences for balancing numbers, International Journal of Contemporary Mathematical Sciences, 7, 18, 2012, 881-889, (2012) MR2905157
  13. Ray, P.K., Balancing and Lucas-balancing sums by matrix methods, Mathematical Reports, 17, 2, 2015, 225-233, (2015) MR3375730
  14. Szynal-Liana, A., Włoch, I., 10.1007/s00006-015-0570-9, Advances in Applied Clifford Algebras, 26, 1, 2016, 435-440, Springer, (2016) MR3460009DOI10.1007/s00006-015-0570-9

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