EN
Determinantal forms and recursive relations of the Delannoy two-functional sequence
Öz
In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms, in terms of the Hessenberg determinants, and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers.
In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms, in terms of the Hessenberg determinants, and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers.
Anahtar Kelimeler
- Delannoy two-functional sequence
- Delannoy one-functional sequence
- Delannoy number
- central Delannoy number
Destekleyen Kurum
Ministry of Science and Technology Republic of China
Proje Numarası
MOST-107-2115-M-017-004-MY2
Teşekkür
Thank a lot
Kaynakça
- \bibitem{banderier} C. Banderier and S. Schwer, \emph{Why Delannoy numbers?}, J. Statist. Plann. Inference \textbf{135} (2005), no.~1, 40\nobreakdash--54; available online at \url{https://doi.org/10.1016/j.jspi.2005.02.004}.
- \bibitem{closed-form-what-why-care} J. M. Borwein and R. E. Crandall, \emph{Closed forms: what they are and why we care}, Notices Amer. Math. Soc. \textbf{60} (2013), no.~1, 50\nobreakdash--65; available online at \url{https://doi.org/10.1090/noti936}.
- \bibitem{Bourbaki-Spain-2004} N. Bourbaki, \emph{Functions of a Real Variable, Elementary Theory}, Translated from the 1976 French original by Philip Spain. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2004; available online at \url{https://doi.org/10.1007/978-3-642-59315-4}.
- \bibitem{CollegeMJ-2002-Cahill} N. D. Cahill, J. R. D'Errico, D. A. Narayan, and J. Y. Narayan, \emph{Fibonacci determinants}, College Math. J. \textbf{33} (2002), no.~3, 221\nobreakdash--225; available online at \url{https://doi.org/10.2307/1559033}.
- \bibitem{M.C.Dagli-Accepted.tex} M. C. Da\u{g}l\i, \emph{A new generalization of Delannoy numbers}, accepted for publication in Indian Journal of Pure and Applied Mathematics.
- \bibitem{gould} H. W. Gould, \textit{Combinatorial Identities: A standardized set of tables listing 500 binomial coefficient summations}, Henry W. Gould, Morgantown, W.Va., 1972.
- \bibitem{guo} V. J. W. Guo, \emph{Proof of Sun's conjectures on integer-valued polynomials}, J. Math. Anal. Appl. \textbf{444} (2016), no.~1, 182\nobreakdash--191; available online at \url{https://doi.org/10.1016/j.jmaa.2016.06.028}.
- \bibitem{higgins} V. Higgins and C. Johnson, \emph{Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices}, Linear Algebra Appl. \textbf{489} (2016), 104\nobreakdash--122; available online at \url{https://doi.org/10.1016/j.laa.2015.10.004}.
Ayrıntılar
Birincil Dil
İngilizce
Konular
Matematik
Bölüm
Araştırma Makalesi
Yayımlanma Tarihi
31 Ağustos 2020
Gönderilme Tarihi
21 Temmuz 2020
Kabul Tarihi
29 Ağustos 2020
Yayımlandığı Sayı
Yıl 2020 Cilt: 4 Sayı: 3
APA
Qi, F., Dağlı, M. C., & Du, W.- shih. (2020). Determinantal forms and recursive relations of the Delannoy two-functional sequence. Advances in the Theory of Nonlinear Analysis and its Application, 4(3), 184-193. https://doi.org/10.31197/atnaa.772734
AMA
1.Qi F, Dağlı MC, Du W shih. Determinantal forms and recursive relations of the Delannoy two-functional sequence. ATNAA. 2020;4(3):184-193. doi:10.31197/atnaa.772734
Chicago
Qi, Feng, Muhammet Cihat Dağlı, ve Wei-shih Du. 2020. “Determinantal forms and recursive relations of the Delannoy two-functional sequence”. Advances in the Theory of Nonlinear Analysis and its Application 4 (3): 184-93. https://doi.org/10.31197/atnaa.772734.
EndNote
Qi F, Dağlı MC, Du W- shih (01 Ağustos 2020) Determinantal forms and recursive relations of the Delannoy two-functional sequence. Advances in the Theory of Nonlinear Analysis and its Application 4 3 184–193.
IEEE
[1]F. Qi, M. C. Dağlı, ve W.- shih Du, “Determinantal forms and recursive relations of the Delannoy two-functional sequence”, ATNAA, c. 4, sy 3, ss. 184–193, Ağu. 2020, doi: 10.31197/atnaa.772734.
ISNAD
Qi, Feng - Dağlı, Muhammet Cihat - Du, Wei-shih. “Determinantal forms and recursive relations of the Delannoy two-functional sequence”. Advances in the Theory of Nonlinear Analysis and its Application 4/3 (01 Ağustos 2020): 184-193. https://doi.org/10.31197/atnaa.772734.
JAMA
1.Qi F, Dağlı MC, Du W- shih. Determinantal forms and recursive relations of the Delannoy two-functional sequence. ATNAA. 2020;4:184–193.
MLA
Qi, Feng, vd. “Determinantal forms and recursive relations of the Delannoy two-functional sequence”. Advances in the Theory of Nonlinear Analysis and its Application, c. 4, sy 3, Ağustos 2020, ss. 184-93, doi:10.31197/atnaa.772734.
Vancouver
1.Feng Qi, Muhammet Cihat Dağlı, Wei-shih Du. Determinantal forms and recursive relations of the Delannoy two-functional sequence. ATNAA. 01 Ağustos 2020;4(3):184-93. doi:10.31197/atnaa.772734
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