有關冪級數及對數級數之間的關係研究

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Title:	有關冪級數及對數級數之間的關係研究
Other Titles:	On relation between the power mean and the logarithmic mean
Authors:	李玄楨;Lee, Hsuan-chen
Contributors:	淡江大學數學學系碩士班楊國勝;Yang, Gou-sheng
Keywords:	冪級數;對數級數;power mean;logarithmic mean
Date:	2006
Issue Date:	2010-01-11 02:56:43 (UTC+8)
Abstract:	假設x及y是不同的正數，則 Mp = Mp (x , y) 稱冪平均數， L = L (x , y) 稱對數平均數。 Chang[2]已證明 : 在某些限制下的x和y，當q<1/3 時，L < Mq，並且證明當 p>0，Mp < L 。我們將證明在某些限制下的x和y，當q <1/6 時，則L < Mq，並且證明當p > 0，L > Mp。 If x , y are distinct positive numbers, then Mp= Mp (x , y) is called the power mean of x and y . L = L (x , y) is called the Logarithmic mean of x and y . Chang[2]has proved that : If L < Mq holds for some q such that q<1/3 ，as well as Mp < L holds for some p such that p>0 under certain restrictions on x and y 。. We shall prove that L < Mq holds for some q such that q <1/6 , as well as L > Mp holds for some p such that p > 0 under certain restrictions on x and y .
Appears in Collections:	[Department of Applied Mathematics and Data Science] Thesis

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