Geodesic
On generalized bihyperbolic Mersenne numbers
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 75-85.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2023.0085-22
Classification : 11B37, 11B39
Keywords: Mersenne number; hyperbolic number; bihyperbolic number; recurrence relation 
@article{10_21136_MB_2023_0085_22,
     author = {Br\'od, Dorota and Szynal-Liana, Anetta},
     title = {On generalized bihyperbolic {Mersenne} numbers},
     journal = {Mathematica Bohemica},
     pages = {75--85},
     publisher = {mathdoc},
     volume = {149},
     number = {1},
     year = {2024},
     doi = {10.21136/MB.2023.0085-22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0085-22/}
}
TY  - JOUR
AU  - Bród, Dorota
AU  - Szynal-Liana, Anetta
TI  - On generalized bihyperbolic Mersenne numbers
JO  - Mathematica Bohemica
PY  - 2024
SP  - 75
EP  - 85
VL  - 149
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0085-22/
DO  - 10.21136/MB.2023.0085-22
LA  - en
ID  - 10_21136_MB_2023_0085_22
ER  - 
%0 Journal Article
%A Bród, Dorota
%A Szynal-Liana, Anetta
%T On generalized bihyperbolic Mersenne numbers
%J Mathematica Bohemica
%D 2024
%P 75-85
%V 149
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0085-22/
%R 10.21136/MB.2023.0085-22
%G en
%F 10_21136_MB_2023_0085_22
Bród, Dorota; Szynal-Liana, Anetta. On generalized bihyperbolic Mersenne numbers. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 75-85. doi : 10.21136/MB.2023.0085-22. http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0085-22/

Cité par Sources :