Jacobsthal matris dizisi ve özellikleri
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Date
2013-04-10
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Selçuk Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Bu çalışmada kısaca bazı sayı dizileri tanımlandıktan sonra Jacobsthal ve Jacobsthal Lucas sayı dizileri ve özellikleri detaylı bir şekilde verilmiştir. Buradan yola çıkarak Jacobsthal ve Jacobsthal Lucas matris dizileri tanımlanıp bu diziler için çeşitli özdeşlikler ve eşitsizlikler elde edilmiş ve bulunan bu özellikler matris cebiri kullanılarak sayı dizileri için de gösterilmiştir. Jacobsthal ve Jacobsthal Lucas matris dizileri için Binet formülü oluşturulmuş bir takım özellikler de bu sayede elde edilmiştir. Ayrıca Jacobsthal ve Jacobsthal Lucas matris dizilerinin kombinatorik temsilleri sunulmuştur. Jacobsthal ve Jacobsthal Lucas matris dizileri için çeşitli kısmi ve sonsuz toplam formülleri elde edilmiş yine matris cebiri yardımıyla sayı dizileri için de toplam formülleri elde edilmiştir. Ayrıca Jacobsthal ve Jacobsthal Lucas matris dizileri için üstel matris dizisi elde edilmiştir. Jacobsthal ve Jacobsthal Lucas matris dizileri yardımıyla genelleştirilmiş Jacobsthal matris dizileri tanımlanmış ve bu üç matris dizisinin birbiriyle olan bağıntıları incelenmiş yukarda bahsedilen birçok özellik genelleştirilmiş Jacobsthal matris dizileri için de oluşturulmuştur.
In this study after some number sequences have been defined briefly, Jacobsthal and Jacobsthal Lucas number sequences and their properties have been given in detail. By setting off here Jacobsthal ve Jacobsthal Lucas matrix sequences have been defined and for these sequences several identities and inequalities have been obtained, and these proporties by using matrix algebra have been used for number sequences. For Jacobsthal and Jacobsthal Lucas matrix sequences Binet formulas have been developed and some proporties have been obtained by using it. Moreever the combinatorics representation of Jacobsthal and Jacobsthal Lucas matrix sequences established. The formulas for the sums of Jacobsthal and Jacobsthal Lucas matrix sequences have been presented, then using matrix algebra these formulas for number sequences have been derived. Also for Jacobsthal and Jacobsthal Lucas matrix sequences exponential matrix sequences have been obtained. Using Jacobsthal and Jacobsthal Lucas matrix sequences generalized Jacobsthal matrix sequences have been defined, and the relations among these three sequences have been analyzed, and a lot of properties had been mentioned upper lines have been given.
In this study after some number sequences have been defined briefly, Jacobsthal and Jacobsthal Lucas number sequences and their properties have been given in detail. By setting off here Jacobsthal ve Jacobsthal Lucas matrix sequences have been defined and for these sequences several identities and inequalities have been obtained, and these proporties by using matrix algebra have been used for number sequences. For Jacobsthal and Jacobsthal Lucas matrix sequences Binet formulas have been developed and some proporties have been obtained by using it. Moreever the combinatorics representation of Jacobsthal and Jacobsthal Lucas matrix sequences established. The formulas for the sums of Jacobsthal and Jacobsthal Lucas matrix sequences have been presented, then using matrix algebra these formulas for number sequences have been derived. Also for Jacobsthal and Jacobsthal Lucas matrix sequences exponential matrix sequences have been obtained. Using Jacobsthal and Jacobsthal Lucas matrix sequences generalized Jacobsthal matrix sequences have been defined, and the relations among these three sequences have been analyzed, and a lot of properties had been mentioned upper lines have been given.
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Fermat, Fibonacci, Jacobsthal, Jacobsthal lucas, Mersenne, Pell sayı dizileri, Pell number sequences
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Citation
Uygun, Ş. (2013). Jacobsthal matris dizisi ve özellikleri. Selçuk Üniversitesi, Yayımlanmış doktora tezi, Konya.
