NEW PROPERTIES AND IDENTITIES FOR BICOMPLEX FIBONACCI FINITE OPERATOR SEQUENCES

Istayan Das^†, Binod Chandra Tripathy^‡, Mausumi Sen^§

Abstract: In this paper, we construct a new class of bicomplex sequences whose components are Fibonacci finite operator sequences. A systematic study of their structural properties is carried out within the framework of the idempotent decomposition of bicomplex numbers. We derive explicit recurrence relations, polynomial representations, and matrix formulations for these bicomplex Fibonacci finite operator sequences. Several identities are established using the associated matrix representation.

Keywords: bicomplex number, Fibonacci number, finite operator, Fibonacci polynomial, matrix representation.
MSC: 11B37, 11B39, 11B83, 05A15.

DOI 10.56082/annalsarscimath.2026.2.241

Read full article

^†dasistayan95@gmail.com, Department of Mathematics, National Institute of Technology Silchar, Silchar 788010, Assam, India
^‡tripathybc@gmail.com, Department of Mathematics, Tripura University, Suryamaninagar, Agartala 799022, Tripura, India
^§mausumi@math.nits.ac.in, Department of Mathematics, National Institute of Technology Silchar, Silchar 788010, Assam, India

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 2, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997