Weerayuth Nilsrakoo, Achariya Nilsrakoo, "Integral Representations of Companion Fibonacci and Pell Numbers," WSEAS Transactions on Mathematics, vol. 25, pp. 169-178, 2026, DOI:10.37394/23206.2026.25.16
Weerayuth Nilsrakoo, Achariya Nilsrakoo. Integral Representations of Companion Fibonacci and Pell Numbers.
WSEAS Transactions on Mathematics. 2026;25:169-178. 10.37394/23206.2026.25.16
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Integral Representations of Companion Fibonacci and Pell Numbers
Authors: ,
Abstract: This paper investigates one-parameter generalizations of the Fibonacci and Pell numbers that preserve
the recurrence relations under arbitrary initial conditions. We present integral representations for the companion
$$k-Pell$$ numbers associated with the $$k-Fibonacci$$ and $$k-Lucas$$ numbers, as well as for those associated with the
$$k-Pell$$ and $$k-Pell-Lucas$$ numbers. Our results extend to all companion numbers of generalized Fibonacci and Pell
sequences.
Keywords:
$$k-Fibonacci$$ number, $$k-Lucas$$ number, $$k-Pell$$ number, $$k-Pell-Lucas$$ number, integral representation
Pages: 169-178 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 25, 2026, Art. #16 DOI: 10.37394/23206.2026.25.16
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