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https://hdl.handle.net/20.500.11851/3490
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DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kılıç, Emrah | - |
dc.contributor.author | Ersanlı, Didem | - |
dc.date.accessioned | 2020-04-27T12:55:04Z | |
dc.date.available | 2020-04-27T12:55:04Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Ersanlı, D. (2019). Lineer indirgeme dizilerinin bazı ters toplamlarının hesaplanması. Ankara: TOBB ETÜ Fen Bilimleri Enstitüsü. [Yayınlanmamış yüksek lisans tezi] | en_US |
dc.identifier.uri | https://hdl.handle.net/20.500.11851/3490 | - |
dc.description.abstract | Bu tezde, $U_{0}=0$, $U_{1}=1$ ve $V_{0}=2$, $V_{1}=p$ başlangıç koşulları olmak üzere her $n\ge{2}$ için \begin{equation*} U_{n}=pU_{n-1}+rU_{n-2}\text{ ve }V_{n}=pV_{n-1}+rV_{n-2}, \end{equation*}% kuralları ile tanımlanan ikinci basamaktan lineer homojen indirgeme dizileri $\lbrace U_{n}\rbrace$ ve $\lbrace V_{n}\rbrace$ ile çalışacağız. Bu dizilerin terimlerini ihtiva eden aşağıdaki ters toplamları hesaplayacağız: \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{V_{k+d+1}}{U_{k+d}U_{k+d+1}U_{k+d+2}}\text{ \ \ \ \ ,\ \ \ \ }\sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k-d}}{U_{k+d}U_{k+d+1}U_{k+d+2}} \end{equation*} ve $X_{n}$, $U_{n}$ ya da $V_{n}$ olmak üzere \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k+c}U_{k+c+1}\ldots U_{k+c+m-1}}{ X_{k+d}X_{k+d+1}\ldots X_{k+d+m+1}}. \end{equation*} | tr_TR |
dc.description.abstract | In this thesis, we will consider second order linear homogeneous recurrences $\lbrace U_{n}\rbrace$ and $\lbrace V_{n}\rbrace$ defined by the rules for $n\ge{2}$ \begin{equation*} U_{n}=pU_{n-1}+rU_{n-2}\text{ and }V_{n}=pV_{n-1}+rV_{n-2}, \end{equation*}% where the initial conditions $U_{0}=0$, $U_{1}=1$ and $V_{0}=2$, $V_{1}=p$, respectively. We will evaluate the following reciprocal sums including terms of these sequences \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{V_{k+d+1}}{U_{k+d}U_{k+d+1}U_{k+d+2}}\text{ \ \ \ \ ,\ \ \ \ \ }\sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k-d}}{U_{k+d}U_{k+d+1}U_{k+d+2}} \end{equation*} and \begin{equation*} \sum\limits_{k=0}^{n}(-r)^{k}\frac{U_{k+c}U_{k+c+1}\ldots U_{k+c+m-1}}{ X_{k+d}X_{k+d+1}\ldots X_{k+d+m+1}} \end{equation*} where $X_{n}$ is $U_{n}$ or $V_{n}$. | en_US |
dc.language.iso | tr | en_US |
dc.publisher | TOBB University of Economics and Technology,Graduate School of Engineering and Science | en_US |
dc.publisher | TOBB ETÜ Fen Bilimleri Enstitüsü | tr_TR |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Reciprocal sums identities | en_US |
dc.subject | q-Calculus | en_US |
dc.subject | Partial fraction decomposition | en_US |
dc.subject | Telescobing idea | en_US |
dc.subject | Ters toplamlar | tr_TR |
dc.subject | q-Analiz | tr_TR |
dc.subject | Basit kesirlere ayırma yöntemi | tr_TR |
dc.subject | Teleskop yaratma | tr_TR |
dc.title | Lineer İndirgeme Dizilerinin Bazı Ters Toplamlarının Hesaplanması | en_US |
dc.title.alternative | Evaluation for Certain Reciprocal Sums of Linear Recurrencesequences | en_US |
dc.type | Master Thesis | en_US |
dc.department | Institutes, Graduate School of Engineering and Science, Mathematics Graduate Programs | en_US |
dc.department | Enstitüler, Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı | tr_TR |
dc.relation.publicationcategory | Tez | en_US |
item.openairetype | Master Thesis | - |
item.languageiso639-1 | tr | - |
item.grantfulltext | open | - |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | Matematik Yüksek Lisans Tezleri / Mathematics Master Theses |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
575694 (1).pdf | Didem Ersanlı_Tez | 1.51 MB | Adobe PDF | View/Open |
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