On generalized bihyperbolic Mersenne numbers

Dorota Bród; Anetta Szynal-Liana

Mathematica Bohemica (2024)

  • Issue: 1, page 75-85
  • ISSN: 0862-7959

Abstract

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In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.

How to cite

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Bród, Dorota, and Szynal-Liana, Anetta. "On generalized bihyperbolic Mersenne numbers." Mathematica Bohemica (2024): 75-85. <http://eudml.org/doc/299220>.

@article{Bród2024,
abstract = {In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.},
author = {Bród, Dorota, Szynal-Liana, Anetta},
journal = {Mathematica Bohemica},
keywords = {Mersenne number; hyperbolic number; bihyperbolic number; recurrence relation},
language = {eng},
number = {1},
pages = {75-85},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized bihyperbolic Mersenne numbers},
url = {http://eudml.org/doc/299220},
year = {2024},
}

TY - JOUR
AU - Bród, Dorota
AU - Szynal-Liana, Anetta
TI - On generalized bihyperbolic Mersenne numbers
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 75
EP - 85
AB - In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
LA - eng
KW - Mersenne number; hyperbolic number; bihyperbolic number; recurrence relation
UR - http://eudml.org/doc/299220
ER -

References

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