本文關(guān)鍵詞：q-Jacobi-Stirling數(shù)　出處：《大連海事大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Stirling 數(shù) q-Jacobi-Stirling 數(shù) q-Legendre-Stirling 數(shù) 遞推關(guān)系 矩陣表示

【摘要】：Legendre-Stirling數(shù)是在Everitt探究經(jīng)典二階勒讓德微分表達(dá)式的譜理論時(shí)提出來(lái)的,而且Legendre-Stirling數(shù)是拉格朗日對(duì)稱式中勒讓德表達(dá)式的積分復(fù)合冪的系數(shù).Jacobi-Stirling數(shù)的概念是Everitt在2007年研究經(jīng)典二階雅各比微分表達(dá)式的譜理論時(shí)首次提出的.Jacobi-Stirling數(shù)是雅各比對(duì)稱式中勒讓德表達(dá)式的積分復(fù)合冪的系數(shù).2012年,Mansour提出了q-類Stirling數(shù)并對(duì)其進(jìn)行了相關(guān)的研究.由于 Jacobi-Stirling 數(shù)、Legendre-Stirling 數(shù)和 類 Stirling 數(shù)與 Stirling 數(shù)有很多相似的性質(zhì),因此,受到很多的人關(guān)注.本文基于q-類Stirling數(shù)定義中基本函數(shù)及 Jacobi-Stirling 數(shù)和 Legendre-Stirling 數(shù)表達(dá)形式,提出了q-Jacobi-Stirling 數(shù)和q-Legendre-Stirling數(shù)的概念,并研究了其相關(guān)性質(zhì).本文的主要工作為以下三個(gè)方面:(1)通過(guò)基本函數(shù)[x]q=1-qx/1-q,引入新的"和函數(shù)"提出了兩類q-Legendre-Stirling數(shù)、q-Jacobi-Stirling數(shù)的概念,推導(dǎo)出了它們滿足的遞推關(guān)系.(2)給出了 第一類 q-Legendre-Stirling 數(shù)和第一類 q-Jacobi-Stirling 數(shù)的一種矩陣表示,證明了 q-Legendre-Stirling數(shù)和q-Jacobi-Stirling數(shù)的若干組合恒等式.(3)研究了兩類q-Legendre-Stirling數(shù)之間的關(guān)系、兩類q-Jacobi-Stirling數(shù)之間的關(guān)系,豐富了類Stirling數(shù)的研究成果.
[Abstract]:Legendre-Stirling number is proposed when Everitt explores the spectrum theory of classical Legendre differential expression. And the concept of Legendre-Stirling number is the coefficient of the integral compound power of Legendre expression in Lagrange symmetry, and the concept of Jacobi-Stirling number is Everi. The Jacobi-Stirling number, first proposed in 2007 when he studied the spectral theory of the classical second-order Yakubi differential expression, is the integral compound power of the Legendre expression in Yakubi's symmetric formula. Coefficient. 2012. Mansour put forward q-like Stirling number and studied it. Because of Jacobi-Stirling number. Legendre-Stirling numbers and similar Stirling numbers have many similar properties with Stirling numbers, so. This paper is based on the definition of q-class Stirling numbers and basic functions and Jacobi-Stirling numbers. Legendre-Stirling number expression. The concepts of q-Jacobi-Stirling number and q-Legendre-Stirling number are proposed. The main work of this paper is as follows: 1) pass through the basic function. [In this paper, the concept of q-Legendre-Stirling number and q-Jacobi-Stirling number is proposed by introducing a new "sum function". The recursion relation that they satisfy. A matrix representation of q-Legendre-Stirling numbers and q-Jacobi-Stirling numbers of the first kind is given. Some combinatorial identities of q-Legendre-Stirling number and q-Jacobi-Stirling number are proved. The relationship between two kinds of q-Legendre-Stirling numbers is studied. The relationship between two classes of q-Jacobi-Stirling numbers enriches the research results of the similar Stirling numbers.
【學(xué)位授予單位】：大連海事大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 李新社;姚俊萍;;第一類Stirling數(shù)公式的猜想及其求解方法[J];哈爾濱師范大學(xué)自然科學(xué)學(xué)報(bào);2014年03期

2 齊登記;;無(wú)符號(hào)第一類Stirling數(shù)的組合數(shù)表示[J];青島科技大學(xué)學(xué)報(bào)(自然科學(xué)版);2011年03期

3 王紅;楊雅琴;王艷輝;;第一類Stirling數(shù)和第二類Stirling數(shù)的關(guān)系式[J];高師理科學(xué)刊;2008年06期

4 楊海明;何世安;鎮(zhèn)松林;蘇政鵬;;斯特林制冷機(jī)振動(dòng)數(shù)學(xué)模型的Laplace變換及仿真[J];低溫與超導(dǎo);2008年04期

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