Some Families of Apéry-Like Fibonacci and Lucas Series
In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed out.
| Published in: | Mathematics |
|---|---|
| Main Authors: | Robert Frontczak, Hari Mohan Srivastava, Živorad Tomovski |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
|
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/14/1621 |
Similar Items
Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$
by: Segun Olofin Akerele, et al.
Published: (2025-04-01)
by: Segun Olofin Akerele, et al.
Published: (2025-04-01)
Three new classes of binomial Fibonacci sums
by: Robert Frontczak
Published: (2024-11-01)
by: Robert Frontczak
Published: (2024-11-01)
Binomial Sum Relations Involving Fibonacci and Lucas Numbers
by: Kunle Adegoke, et al.
Published: (2023-11-01)
by: Kunle Adegoke, et al.
Published: (2023-11-01)
Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers
by: Yulei Chen, et al.
Published: (2024-03-01)
by: Yulei Chen, et al.
Published: (2024-03-01)
General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
by: R. Frontczak, et al.
Published: (2021-06-01)
by: R. Frontczak, et al.
Published: (2021-06-01)
On some series involving the binomial coefficients $binom{3n}{n}$
by: Kunle Adegoke, et al.
Published: (2024-05-01)
by: Kunle Adegoke, et al.
Published: (2024-05-01)
Remarks on an Identity of Anastase and Díaz-Barrero
by: Horst Alzer, et al.
Published: (2025-06-01)
by: Horst Alzer, et al.
Published: (2025-06-01)
Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions
by: A. D. Godase
Published: (2024-03-01)
by: A. D. Godase
Published: (2024-03-01)
Cubic binomial Fibonacci sums
by: Kunle Adegoke, et al.
Published: (2021-12-01)
by: Kunle Adegoke, et al.
Published: (2021-12-01)
Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
by: Yasemin Taşyurdu, et al.
Published: (2023-02-01)
by: Yasemin Taşyurdu, et al.
Published: (2023-02-01)
Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
by: Dongwei Guo, et al.
Published: (2022-07-01)
by: Dongwei Guo, et al.
Published: (2022-07-01)
Fifteen series on harmonic numbers and quintic central binomial coefficients
by: Chunli Li, et al.
Published: (2025-07-01)
by: Chunli Li, et al.
Published: (2025-07-01)
3x3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers
by: Sinan Karakaya, et al.
Published: (2018-12-01)
by: Sinan Karakaya, et al.
Published: (2018-12-01)
New Harmonic Number Series
by: Kunle Adegoke, et al.
Published: (2025-03-01)
by: Kunle Adegoke, et al.
Published: (2025-03-01)
Hybrid hyper-Fibonacci and hyper-Lucas numbers
by: Yasemin Alp
Published: (2023-03-01)
by: Yasemin Alp
Published: (2023-03-01)
On a Family of Infinite Series with Reciprocal Catalan Numbers
by: Kunle Adegoke, et al.
Published: (2022-04-01)
by: Kunle Adegoke, et al.
Published: (2022-04-01)
Construction of dual-generalized complex Fibonacci and Lucas quaternions
by: G.Y. Şentürk, et al.
Published: (2022-11-01)
by: G.Y. Şentürk, et al.
Published: (2022-11-01)
A note on Fibonacci and Lucas number of domination in path
by: Leomarich F Casinillo
Published: (2018-10-01)
by: Leomarich F Casinillo
Published: (2018-10-01)
Transmission of Time and Position Variable Cryptology in Fibonacci and Lucas Number Series with Music
by: Firdevs Nur Algül, et al.
Published: (2021-04-01)
by: Firdevs Nur Algül, et al.
Published: (2021-04-01)
A Combinatorial Proof of a Result on Generalized Lucas Polynomials
by: Laugier Alexandre, et al.
Published: (2016-09-01)
by: Laugier Alexandre, et al.
Published: (2016-09-01)
Fibonacci and Lucas identities derived via the golden ratio
by: Kunle Adegoke
Published: (2022-08-01)
by: Kunle Adegoke
Published: (2022-08-01)
Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences
by: Alparslan Kargın, et al.
Published: (2019-10-01)
by: Alparslan Kargın, et al.
Published: (2019-10-01)
Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals
by: Waleed Mohamed Abd-Elhameed, et al.
Published: (2022-07-01)
by: Waleed Mohamed Abd-Elhameed, et al.
Published: (2022-07-01)
Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions
by: Ramírez José L.
Published: (2015-06-01)
by: Ramírez José L.
Published: (2015-06-01)
Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions
by: Engin Özkan, et al.
Published: (2024-12-01)
by: Engin Özkan, et al.
Published: (2024-12-01)
Identities for Fibonacci and Lucas numbers
by: George Grossman, et al.
Published: (2023-11-01)
by: George Grossman, et al.
Published: (2023-11-01)
An Alternating Sum of Fibonacci and Lucas Numbers of Order <i>k</i>
by: Spiros D. Dafnis, et al.
Published: (2020-09-01)
by: Spiros D. Dafnis, et al.
Published: (2020-09-01)
Fibonacci sums and divisibility properties
by: Kunle Adegoke, et al.
Published: (2023-12-01)
by: Kunle Adegoke, et al.
Published: (2023-12-01)
On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
by: S.E. Rihane
Published: (2021-06-01)
by: S.E. Rihane
Published: (2021-06-01)
Vieta's triangular array and a related family of polynomials
by: Neville Robbins
Published: (1991-01-01)
by: Neville Robbins
Published: (1991-01-01)
Multiple Sums of Circular Binomial Products
by: Marta Na Chen, et al.
Published: (2024-06-01)
by: Marta Na Chen, et al.
Published: (2024-06-01)
Series of Convergence Rate −1/4 Containing Harmonic Numbers
by: Chunli Li, et al.
Published: (2023-05-01)
by: Chunli Li, et al.
Published: (2023-05-01)
Dirichlet series and series with Stirling numbers
by: Khristo Boyadzhiev
Published: (2023-04-01)
by: Khristo Boyadzhiev
Published: (2023-04-01)
Binomial Series Involving Harmonic-like Numbers
by: Chunli Li, et al.
Published: (2024-02-01)
by: Chunli Li, et al.
Published: (2024-02-01)
Fibonacci Sums Modulo 5
by: Adegoke Kunle, et al.
Published: (2024-06-01)
by: Adegoke Kunle, et al.
Published: (2024-06-01)
Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
by: Emrah Polatlı
Published: (2023-09-01)
by: Emrah Polatlı
Published: (2023-09-01)
A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers
by: Bahar Kuloğlu
Published: (2025-03-01)
by: Bahar Kuloğlu
Published: (2025-03-01)
Hybrid convolutions on Pell and Lucas polynomials
by: Dongwei Guo, et al.
Published: (2021-07-01)
by: Dongwei Guo, et al.
Published: (2021-07-01)
On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers
by: Younseok Choo
Published: (2021-02-01)
by: Younseok Choo
Published: (2021-02-01)
A partial recurrence Fibonacci link
by: Anthony G. Shannon, et al.
Published: (2024-09-01)
by: Anthony G. Shannon, et al.
Published: (2024-09-01)
Similar Items
-
Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$
by: Segun Olofin Akerele, et al.
Published: (2025-04-01) -
Three new classes of binomial Fibonacci sums
by: Robert Frontczak
Published: (2024-11-01) -
Binomial Sum Relations Involving Fibonacci and Lucas Numbers
by: Kunle Adegoke, et al.
Published: (2023-11-01) -
Combinatorial identities concerning trigonometric functions and Fibonacci/Lucas numbers
by: Yulei Chen, et al.
Published: (2024-03-01) -
General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
by: R. Frontczak, et al.
Published: (2021-06-01)
