New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries

ömür, neşe; koparal, sibel; Kılıç, Emrah

doi:10.15672/hujms.473495

New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries

Emrah Kılıç, (TOBB Ekonomi ve Teknoloji Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Bölümü, Ankara, Türkiye)

Neşe Ömür, (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)

Sibel Koparal (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)

Hacettepe Journal of Mathematics and Statistics

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Yıl: 2020 Cilt: 49 Sayı: 2 Sayfa Aralığı: 684 - 694 Metin Dili: İngilizce DOI: 10.15672/hujms.473495 İndeks Tarihi: 29-07-2022

New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries

Öz:

In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their $LU$-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in $q$-word and then use the celebrated Zeilberger algorithm to prove required $q$-identities.

Anahtar Kelime: q-analogues Zeilberger’s algorithm Generalized Filbert matrix LU-decomposition Computer algebra system (CAS)

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Kılıç E, ömür n, koparal s (2020). New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. , 684 - 694. 10.15672/hujms.473495
Chicago	Kılıç Emrah,ömür neşe,koparal sibel New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. (2020): 684 - 694. 10.15672/hujms.473495
MLA	Kılıç Emrah,ömür neşe,koparal sibel New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. , 2020, ss.684 - 694. 10.15672/hujms.473495
AMA	Kılıç E,ömür n,koparal s New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. . 2020; 684 - 694. 10.15672/hujms.473495
Vancouver	Kılıç E,ömür n,koparal s New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. . 2020; 684 - 694. 10.15672/hujms.473495
IEEE	Kılıç E,ömür n,koparal s "New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries." , ss.684 - 694, 2020. 10.15672/hujms.473495
ISNAD	Kılıç, Emrah vd. "New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries". (2020), 684-694. https://doi.org/10.15672/hujms.473495

APA	Kılıç E, ömür n, koparal s (2020). New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics, 49(2), 684 - 694. 10.15672/hujms.473495
Chicago	Kılıç Emrah,ömür neşe,koparal sibel New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics 49, no.2 (2020): 684 - 694. 10.15672/hujms.473495
MLA	Kılıç Emrah,ömür neşe,koparal sibel New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics, vol.49, no.2, 2020, ss.684 - 694. 10.15672/hujms.473495
AMA	Kılıç E,ömür n,koparal s New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 684 - 694. 10.15672/hujms.473495
Vancouver	Kılıç E,ömür n,koparal s New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 684 - 694. 10.15672/hujms.473495
IEEE	Kılıç E,ömür n,koparal s "New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries." Hacettepe Journal of Mathematics and Statistics, 49, ss.684 - 694, 2020. 10.15672/hujms.473495
ISNAD	Kılıç, Emrah vd. "New analogues of the Filbert and Lilbert matrices via products of two $k$-tuples asymmetric entries". Hacettepe Journal of Mathematics and Statistics 49/2 (2020), 684-694. https://doi.org/10.15672/hujms.473495