關(guān)于e和ex級(jí)數(shù)型展開式的規(guī)律分析_數(shù)學(xué)專業(yè)畢業(yè)論文-全文預(yù)覽
【正文】 )!1(1)!2(13)!3(1())!1(1)!2(1)!2(1)!2(1)!3(1())!1(1)!2(1()!1(1)1)(1()!1(!000002033????????????????????????????????????????????????? 第 4 頁(yè) ennnnnnnnnnnnnnnnnnnnnnnnnnnnnnnannnnnn15))!1(1)!2(17)!3(16)!4(1())!1(1)!2(1)!2(1)!2(1)!2(1)!2(1)!2(1)!2(1)!3(1)!3(1)!3(1)!3(1)!3(1)!3(1)!4(1())!1()!2(()!1()1()!1(!0020202203044?????????????????????????????????????????????????????????????????????? ?? 猜想 1： ??????????????????????????032010)!(1))!( 1)!3( 1)!2( 1)!1( 1(!nkjkkkknknkkjnbknbnbnbnbnna ?? 其中 kjNjk ??? 0, 且 。 Computer science of xxxxxxx Instructor:xx Abstract: As everyone knows , xe form of power series expansion : 2301 1 1 1 11 1 ! 2! 3 ! ! !x n nne x x x x xnn??? ? ? ? ? ? ? ? ? Among them, take 1?x , are: 01 1 1 1 1 11 1 ! 2! 3 ! 4! ! !ne nn??? ? ? ? ? ? ? ? ? ? Below, we ask: what is the progression ???0 !n nn ， ???02!n nn ， ???03!n nn ， ? ， ???0 !nknn . In fact, research of the power function progression ),3,2,1,0(!0 ??????? kxnn nnk more convenient, because we can use calculus as a tool. For ??,3,2,1,0?k , nnkk xnnxa ?????0 !)(, due to the radius of convergence of the right end power series are as follows: ??r , Therefore, )(xak to Rx?? is particular, when 1?x , ???? 0 !)1( nkk nna. Demonstrated by calculation, this paper concludes that: xkk exPxa ?? )()( , Among them )(xPk is about x k polynomial of the )(xPk of polynomial coefficient into a matrix of infinite order, remember to ? ? NikkiaA ?? , , of the matrix rows, columns and oblique direction of A analysis, summarized, to draw 第 3 頁(yè) conclusions. Key words: The development of power series 。特別地，當(dāng) 1?x 時(shí)，有00 !)1( anna nkk ????? 。 對(duì) ??,3,2,1,0?k 令 nnkk xnnxa ?????0 !)( ，由于右端冪級(jí)數(shù)的收斂半徑為： ??r ，故 )(xak 對(duì) Rx?? 有定義。 【關(guān)鍵詞】： 冪級(jí)數(shù)的展開； 微積分 ；遞推公式 ； 多項(xiàng)式；矩陣 第 2 頁(yè) About e and xe series type expansion analysis of the law xxx Grade 20xx, Math class, mathematics and applied mathematics major， School of Mathematics amp。 Polynomial 。 在驗(yàn)證猜想 1 之前，我們先來討論當(dāng) 1?x 時(shí)的情形， 即 當(dāng) 1?x 時(shí)，有： 令 xnn exnxa ?? ???00 !1)( nn xnnxa ???? 01 !)( nn xnnxa ???? 022 !)( nn xnnxa ???? 033 !)
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