This mathematical study examines one-parameter generalisations of Fibonacci and Pell sequences that preserve their recurrence relations under arbitrary initial conditions, deriving integral representations for several companion-sequence families.
Key findings
- The study derives integral representations spanning multiple families of generalised companion sequences while preserving their recurrence structure. The outputs are mathematical theorems and identities rather than empirical findings.
Why this matters globally
The representations may support further study of analytic properties, generating functions, identities and algorithms for recurrence sequences. Broader impact depends on subsequent use and specialist scrutiny.
Thai researcher contribution
Weerayuth Nilsrakoo of Ubon Ratchathani University and Achariya Nilsrakoo of Ubon Ratchathani Rajabhat University contributed the mathematical results.
Limitations to consider
The work is theoretical, with limited computational or applied evidence in the available record. It does not benchmark algorithms, numerical sensitivity or practical use, and novelty relative to the extensive sequence-identity literature requires specialist assessment.