Normal view MARC view ISBD view

Lineer indirgeme dizilerinin bazı ters toplamlarının hesaplanması / Didem Ersanlı ; thesis advisor Emrah Kılıç.

By: Ersanlı, Didem [author].
Contributor(s): Kılıç, Emrah [advisor] | TOBB Ekonomi ve Teknoloji Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Enstitüsü.
Material type: materialTypeLabelBookPublisher: Ankara : TOBB ETÜ Fen Bilimleri Enstitüsü, 2019Description: ix, 41 pages : illustrations ; 29 cm.Content type: text Media type: unmediated Carrier type: volumeOther title: Evaluation for certain reciprocal sums of linear recurrencesequences [Parallel title].Subject(s): Tezler, Akademik | Ters toplamlar | Basit kesirlere ayırma yöntemi | Teleskop yaratma | q-Analiz | Reciprocal sums identities | Partial fraction decomposition | Telescobing idea | q-CalculusOnline resources: Ulusal Tez Merkezi Dissertation note: Tez (Yüksek Lisans)--TOBB ETÜ Fen Bilimleri Enstitüsü Temmuz 2019 Summary: 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*}Summary: 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 $V_{n}$.
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Current location Collection Call number Copy number Status Date due Barcode
Thesis Thesis Merkez Kütüphane
Tez Koleksiyonu / Thesis Collection
Tezler TEZ TOBB FBE MAT YL’19 ERS (Browse shelf) 1 Ödünç Verilemez-Tez / Not For Loan-Thesis TZ01043

Tez (Yüksek Lisans)--TOBB ETÜ Fen Bilimleri Enstitüsü Temmuz 2019

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*}

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 $V_{n}$.

This software was implemented, installed by Devinim Software Training Consulting .