本文選題：伽瑪函數(shù) + 完全單調(diào)函數(shù)��； 參考：《天津工業(yè)大學(xué)》2017年碩士論文

【摘要】：近些年來(lái),國(guó)內(nèi)外越來(lái)越多的著名數(shù)學(xué)學(xué)者從事伽瑪函數(shù)和Ψ函數(shù)(對(duì)數(shù))完全單調(diào)性方面的研究。(對(duì)數(shù))完全單調(diào)性已經(jīng)成為數(shù)學(xué)知識(shí)新增熱點(diǎn)之一。與伽瑪函數(shù)和嶺函數(shù)相關(guān)函數(shù)的完全單調(diào)性以及對(duì)數(shù)完全單調(diào)性,對(duì)一些重要不等式的證明、加強(qiáng)與推廣,具有十分重要的作用。在組合數(shù)學(xué)中,Bell多項(xiàng)式和Catalan數(shù)的特殊序列均滿足大量的恒等式,并且在數(shù)論、數(shù)值分析等領(lǐng)域都有廣泛的應(yīng)用。所以本文主要內(nèi)容都有涉及以上知識(shí)。本文主要分為五部分,第一部分主要介紹研究背景,第二部分主要修正了關(guān)于q伽瑪函數(shù)的完全單調(diào)性質(zhì)證明的兩篇文章,第三部分主要研究的是一個(gè)特殊的函數(shù)成為對(duì)數(shù)完全單調(diào)函數(shù)的充分條件和必要條件,這個(gè)函數(shù)是由伽瑪函數(shù)和Catalan數(shù)演變得到的。第四部分介紹了第二類Bell多項(xiàng)式特殊值的顯示表達(dá)式,用貝塞爾多項(xiàng)式連接,且應(yīng)用著名的Faadi Bruno公式,給出了Catalan數(shù)新的表達(dá)形式,而且計(jì)算出一些基本初等函數(shù)的任意高階導(dǎo)數(shù)。其中基本初等函數(shù)包括正弦函數(shù)、余弦函數(shù)、指數(shù)函數(shù)、對(duì)數(shù)函數(shù)等。第五部分是總結(jié)和展望。
[Abstract]:In recent years, more and more famous mathematics scholars at home and abroad are engaged in the study of complete monotonicity of gamma function and 蠄 function (logarithm). (logarithm) complete monotonicity has become one of the new hotspots of mathematical knowledge. The complete monotonicity and logarithmic complete monotonicity of the correlation functions with gamma function and ridge function play a very important role in proving some important inequalities, strengthening and extending them. In combinatorial mathematics, the special sequences of Bell polynomials and Catalan numbers satisfy a large number of identities and are widely used in the fields of number theory and numerical analysis. So the main content of this paper involves the above knowledge. This paper is divided into five parts. The first part mainly introduces the background of the research. The second part mainly corrects two articles about the proof of the completely monotone property of Q gamma function. The third part mainly studies the sufficient conditions and necessary conditions for a special function to become logarithmic completely monotone function, which is derived from gamma function and Catalan number. In the fourth part, we introduce the expression of the special value of the second kind of Bell polynomials, which are connected by Bessel polynomials, and give a new expression of Catalan numbers by using the famous Faadi Bruno formula. Moreover, arbitrary higher order derivatives of some basic elementary functions are calculated. The basic elementary functions include sinusoidal function, cosine function, exponential function, logarithmic function and so on. The fifth part is the summary and prospect.
【學(xué)位授予單位】：天津工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O174.6

【相似文獻(xiàn)】

中國(guó)期刊全文數(shù)據(jù)庫(kù) 前9條

1 張素玲;陳超平;祁鋒;;關(guān)于伽瑪函數(shù)的單調(diào)性質(zhì)(英文)[J];大學(xué)數(shù)學(xué);2006年04期

2 孫建設(shè);;關(guān)于伽瑪函數(shù)和不完全伽瑪函數(shù)單調(diào)性的注記[J];純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué);2007年01期

3 夏慧異;;伽瑪函數(shù)相關(guān)問題的研究[J];池州學(xué)院學(xué)報(bào);2010年06期

4 沈仲達(dá);伽瑪函數(shù)和誤差函數(shù)在物理教學(xué)中的應(yīng)用──物理概念和數(shù)學(xué)方法相結(jié)合之二[J];紹興文理學(xué)院學(xué)報(bào)(自然科學(xué)版);1997年05期

5 王琪;張國(guó)林;;歐拉積分在積分學(xué)中的應(yīng)用[J];科教文匯(下旬刊);2011年06期

6 王日棟;;關(guān)于兩個(gè)復(fù)合函數(shù)的不等式性質(zhì)[J];赤峰學(xué)院學(xué)報(bào)(自然科學(xué)版);2010年12期

7 李力;;伽瑪函數(shù)與一個(gè)力學(xué)問題的解析解[J];物理與工程;2012年03期

8 吳明官，，李彥興;不完全伽瑪函數(shù)的快速算法[J];水文;1994年01期

9 ;[J];;年期

中國(guó)碩士學(xué)位論文全文數(shù)據(jù)庫(kù) 前2條

1 劉方方;關(guān)于Q伽瑪函數(shù)和第二類BELL多項(xiàng)式的某些性質(zhì)和應(yīng)用[D];天津工業(yè)大學(xué);2017年

2 安苗青;關(guān)于伽瑪函數(shù)和Barnes G-函數(shù)的完全單調(diào)性質(zhì)和不等式[D];河南理工大學(xué);2010年

本文編號(hào)：1990172