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關(guān)于e和ex級(jí)數(shù)型展開(kāi)式的規(guī)律分析_數(shù)學(xué)專業(yè)畢業(yè)論文-展示頁(yè)

2025-07-25 13:43本頁(yè)面
  

【正文】 2 3( ) ( )[ ( 1 510 9075 31080 34755 158763234 288 9 ) ( 255 30257770 6951 2646 462 36 ) ]( 510 9075 31080 34755 158763234 288 9 ) ( 255 3xxxa x x a xx x x x x xx x e x x xx x x x x x ex x x x x xx x e x x??? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?45 6 7 8 9 102 3 4 5 67 8 9 100257770 6951 2646 462 36 )( 511 9330 34105 42525 228275880 750 45 )xxxx x x x x x ex x x x x xx x x x e? ? ? ? ? ?? ? ? ? ? ?? ? ? ? 由上述計(jì)算,我們猜想 2: xkk exPxa ?? )()( 其中, )(xPk 是關(guān)于 x 的多項(xiàng)式 。答案:猜想 1 正確。 Matrix 在微積分中,我們知道: 01 1 1 1 1 11 1 ! 2! 3 ! 4! ! !ne nn??? ? ? ? ? ? ? ? ? ? 更一般地,有: 2301 1 1 1 11 1 ! 2! 3 ! ! !x n nne x x x x xnn??? ? ? ? ? ? ? ? ?下面,我們首先來(lái)研究,當(dāng) 1?x 時(shí), ???? 0 !1n ne : 令 ena n ?????00 !1 ennna nn ???? ?? ???? 001 )!1( 1! ennn nnna nnn 2))!1( 1)!2( 1()!1(! 00022 ???????? ????????? ennnnnnnnnnnnnnnnnnannnnnn5))!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 。The recursive formula 。 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
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