Araştırma Makalesi
Yıl 2023,
Cilt: 52 Sayı: 1, 62 - 72, 15.02.2023
Öz
By making use of known identities of terminating well-poised $q$-series,
we shall demonstrate several remarkable summation formulae involving
products of two Fibonomial/Lucanomial coefficients or quotients
of two such coefficients over a third one.
Anahtar Kelimeler
Gaussian coefficient $q$-binomial coefficient Well-poised $q$-series Fibonomial coefficient Lucanomial coefficient
Kaynakça
- [1] W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935
- [2] W. N. Bailey, On the analogue of Dixon’s theorem for bilateral basic hypergeometric series, Quart. J. Math. 1 (1), 318–320, 1950.
- [3] D. M. Bressoud, Almost poised basic hypergeometric series, Proc. Indian Acad. Sci. (Math. Sci.) 97 (1), 61–66, 1987.
- [4] L. Carlitz, The characteristic polynomial of a certain matrix of binomial coefficients, The Fibonacci Quarterly, 3, 81–89, 1965.
- [5] L. Carlitz, Some formulas of F. H. Jackson, Monatsh. Math. 73, 193–198, 1969.
- [6] W. Chu, Basic almost poised hypergeometric series, Mem. Amer. Math. Soc. Vol. 642, 1998.
- [7] W. Chu and E. Kılıç, Cubic sums of q-binomial coefficients and the Fibonomial coefficients, Rocky Mountain J. Math. 49 (8), 2557 - 2569, 2019.
- [8] W. Chu and E. Kılıç, Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients, The Ramanujan Journal, 51 (2), 229-243, 2020.
- [9] W. Chu and C. Y. Wang, Bilateral inversions and terminating basic hypergeometric series identities, Discrete Math. 309 (12), 3888–3904, 2009.
- [10] G. Gasper and M. Rahman, Basic Hypergeometric Series (2nd ed.), Cambridge University Press, Cambridge, 2004.
- [11] A. F. Horadam and B. J. M. Mahon, Pell and Pell–Lucas polynomials, Fibonacci Quart. 23 (1), 7–20, 1985.
- [12] D. Jarden, Recurring sequences, Riveon Lematematika, Jerusalem, Israel, 1958.
- [13] E. Kılıç, The generalized Fibonomial matrix, European J. Combin. 31 (1), 193–209, 2010.
- [14] N. N. li and W. Chu, q-Derivative operator proof for a conjecture of Melham, Discrete Applied Mathematics, 177, 158–164, 2014.
- [15] B. J. M. Mahon and A. F. Horadam, Inverse trigonometrical summation formulas involving Pell polynomials, Fibonacci Quart. 23 (4), 319–324, 1985.
- [16] J. Seibert and P. Trojovsky, On some identities for the Fibonomial coefficients, Math. Slovaca 55, 9–19, 2005.
- [17] P. Trojovsky, On some identities for the Fibonomial coefficients via generating function, Discrete Appl. Math. 155 (15), 2017–2024, 2007.
Yıl 2023,
Cilt: 52 Sayı: 1, 62 - 72, 15.02.2023
Öz
Kaynakça
- [1] W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935
- [2] W. N. Bailey, On the analogue of Dixon’s theorem for bilateral basic hypergeometric series, Quart. J. Math. 1 (1), 318–320, 1950.
- [3] D. M. Bressoud, Almost poised basic hypergeometric series, Proc. Indian Acad. Sci. (Math. Sci.) 97 (1), 61–66, 1987.
- [4] L. Carlitz, The characteristic polynomial of a certain matrix of binomial coefficients, The Fibonacci Quarterly, 3, 81–89, 1965.
- [5] L. Carlitz, Some formulas of F. H. Jackson, Monatsh. Math. 73, 193–198, 1969.
- [6] W. Chu, Basic almost poised hypergeometric series, Mem. Amer. Math. Soc. Vol. 642, 1998.
- [7] W. Chu and E. Kılıç, Cubic sums of q-binomial coefficients and the Fibonomial coefficients, Rocky Mountain J. Math. 49 (8), 2557 - 2569, 2019.
- [8] W. Chu and E. Kılıç, Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients, The Ramanujan Journal, 51 (2), 229-243, 2020.
- [9] W. Chu and C. Y. Wang, Bilateral inversions and terminating basic hypergeometric series identities, Discrete Math. 309 (12), 3888–3904, 2009.
- [10] G. Gasper and M. Rahman, Basic Hypergeometric Series (2nd ed.), Cambridge University Press, Cambridge, 2004.
- [11] A. F. Horadam and B. J. M. Mahon, Pell and Pell–Lucas polynomials, Fibonacci Quart. 23 (1), 7–20, 1985.
- [12] D. Jarden, Recurring sequences, Riveon Lematematika, Jerusalem, Israel, 1958.
- [13] E. Kılıç, The generalized Fibonomial matrix, European J. Combin. 31 (1), 193–209, 2010.
- [14] N. N. li and W. Chu, q-Derivative operator proof for a conjecture of Melham, Discrete Applied Mathematics, 177, 158–164, 2014.
- [15] B. J. M. Mahon and A. F. Horadam, Inverse trigonometrical summation formulas involving Pell polynomials, Fibonacci Quart. 23 (4), 319–324, 1985.
- [16] J. Seibert and P. Trojovsky, On some identities for the Fibonomial coefficients, Math. Slovaca 55, 9–19, 2005.
- [17] P. Trojovsky, On some identities for the Fibonomial coefficients via generating function, Discrete Appl. Math. 155 (15), 2017–2024, 2007.
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Şubat 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 52 Sayı: 1 |