TY  - JOUR
T1  - THE HYBRID FORM OF THE HYPERBOLIC HORADAM MATRIX FUNCTIONS
AU  - Mersin, Efruz Özlem
PY  - 2025
DA  - October
Y2  - 2025
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 2505
EP  - 2518
VL  - 15
IS  - 10
LA  - en
AB  - In the present paper, a special type of hybrid number is introduced whose components are the hyperbolic Horadam sine and cosine matrix functions. These hybrid numbers and their symmetrical forms are explored in detail, and their recursive relations as well as hyperbolic properties are investigated. The paper also includes the Cassini, Catalan, and De Moivre identities, along with the Pythagorean Theorem, all for the hybrid form of the hyperbolic Horadam sine and cosine matrix functions. Furthermore, the hybrid forms of the quasi-sine Horadam matrix function and three-dimensional Horadam matrix spiral related to these matrix functions are presented, offering new insights into their mathematical properties.
KW  - Horadam number sequence
KW  - Hybrid numbers
KW  - Hyperbolic matrix functions
KW  - Matrix exponential
KW  - Trigonometric matrix functions
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UR  - https://dergipark.org.tr/en/pub/twmsjaem/issue//1795314
L1  - https://dergipark.org.tr/en/download/article-file/5293091
ER  -