頁籤選單縮合
題名 | 用MATHEMATICA對自然數之負次方和的探討=Exploring the Sums of Negative Powers of Positive Integers with MATHEMATICA |
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作者 | 沈淵源; | 書刊名 | 東海科學 |
卷期 | 5 民92.07 |
頁次 | 頁55-70 |
分類號 | 311.27 |
關鍵詞 | 自然數; 負次方和; 級數; |
語文 | 中文(Chinese) |
中文摘要 | 透過數學運算大師MATHEMATICA所提供的之值,我們一起來探討這個無窮級數之和的公式。當s=2m為正偶數之時,MATHEMATICA告訴我們ζ(2)為n2m的有理數倍。在數學運算大師MATHEMATICA的協助之下,我們將帶領由這些個別的函數值ζ(2m)來拼裝出整個公式的形式圖樣。至於s為正奇數之時,MATHEMATICA卻不作任何的表態。事實上,連最簡單的ζ(3)到目前為止還是沒有一個公式如ζ(2m)者存在。這有待您來繼續努力,無限的機會就擺在你面前,不是嗎? |
英文摘要 | We explore a formula for the sum of the infinite series ζ(s)= according to the values provided by MATHEMATICA. When s=2m is an even positive integer. MATHEMATICA tells us that ζ(2m) is just a rational multiple ofπ2m. From these individual function values, with the help of MATHEMATICA, we will guide you to see the pattern of the whole formula. On the other hand, when s is an odd positive integer, MATHEMATICA tells us nothing. In fact, there is no such formula exists even for the simplest ζ(3). The reason remains unknown, so still a lot of chances are waiting for you. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。