Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 49 min ago
PreprintCC BY 4.0arXiv

An Integral Representation of the Generalized Fibonacci Numbers

  • Bikash Chakraborty
  • Kalyan Barman
  • Soumon Roy
  • Ritam Sinha
Open at sourcePDFDOICite

Abstract

In this note, we present an integral representation of the k-generalized Fibonacci sequence and provide a proof using contour integration. This representation enables the derivation of several known identities and a Binet-type formula related to the k-generalized Fibonacci sequence.

Versions

Related

  1. A number field extension of Ramanujan's identity and its integral representation via the generalized Riemann Ξ-function
    Diksha Rani Bansal
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Infinite Series About Reciprocal Products of Fibonacci and Lucas Numbers
    Marta Na Chen, Wenchang Chu
    AxiomsPeer-reviewedCC BY 4.0Algebra & number theoryCrossref
  3. The Fibonacci numbers are not 3-accessible
    William J. Wesley
    arXivPreprintCC BY-NC-ND 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. The Fibonacci numbers are not an additive uniqueness set for multiplicative functions
    Poo-Sung Park
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Asymptotics for partitions over the Fibonacci numbers and related sequences, II
    Michael Coons, Simon Kristensen, Mathias L. Laursen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{chakraborty2026integral,
  title = {{An Integral Representation of the Generalized Fibonacci Numbers}},
  author = {Bikash Chakraborty and Kalyan Barman and Soumon Roy and Ritam Sinha},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25106},
  eprint = {2609.25106},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25106},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An Integral Representation of the Generalized Fibonacci Numbers
AU  - Bikash Chakraborty
AU  - Kalyan Barman
AU  - Soumon Roy
AU  - Ritam Sinha
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.25106
UR  - https://arxiv.org/abs/2609.25106
AB  - In this note, we present an integral representation of the k-generalized Fibonacci sequence and provide a proof using contour integration. This representation enables the derivation of several known identities and a Binet-type formula related to the k-generalized Fibonacci sequence.
ER  -