關于e和ex級數型展開式的規(guī)律分析_數學專業(yè)畢業(yè)論文-免費閱讀
【正文】 在定理 1 的基礎上我們得到了關于多項式 )(xPk 的遞推公式，即定理 2。 有定理 2 知： 1)(0 ?xP xxP ?)(1 22 )( xxxP ?? 323 3)( xxxxP ??? 4324 67)( xxxxxP ???? 54325 102515)( xxxxxxP ????? 654326 15659031)( xxxxxxxP ?????? 7654327 211 4 03 5 03 0 163)( xxxxxxxxP ??????? 87654328 2826610501701966127)( xxxxxxxxxP ???????? 987654329 364622646695177703025255)( xxxxxxxxxxP ????????? 109876543210457505880 2282742525341059330511)( xxxx xxxxxxxP ???? ?????? ?? 于是，有 xx exPexa ??? )()( 00 xx exPexxa ???? )()( 11 第 10 頁 xx exPexxxa ????? )()()( 222 xx exPexxxxa ?????? )()3()( 3323 xx exPexxxxxa ??????? )()67()( 44324 xx exPexxxxxxa ???????? )()102515()( 554325 xx exPexxxxxxxa ????????? )()15659031()( 6654326 xx exPexxxxxxxxa ?????????? )()2114035030163()( 77654327 xxexPexxxxxxxxxa???????????)()2826610501701966127()(887654328xxexPexxxxxxxxxxa????????????)()364 622 64 66 95 17 77 03 02 52 55()(9987654329 xxexPexxxxxxxxxxxa?????????????)()457505 8 802 2 82 74 2 52 53 4 10 59 3 30511()(10109876543210 ?? 故，有 xkk exPxa ?? )()( 成立，且 )(xPk 是關于 x 的 k 次 多項式 。 Polynomial 。 對 ??,3,2,1,0?k 令 nnkk xnnxa ?????0 !)( ，由于右端冪級數的收斂半徑為： ??r ，故 )(xak 對 Rx?? 有定義。 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 conclusions. Key words: The development of power series 。 第 6 頁 由 定理 1 可知： 010221()( ) ( )( ) ( ) ( ) ( )xxx x xa x ea x x a x x ea x x a x x e x e x x e?????? ? ? ? ? ? ? ? ?? ? ? ?? ?2322 2 323( ) ( ) 1 223xxxxxa x x a x x x e x x ex x e x x ex x x e? ??? ? ? ? ???? ? ? ?? ? ? ? ? ? ?? ? ? ?? ?432 2 32 3 2 3 42 3 4( ) ( )1 6 3 36 3 376xxxxxx x a xx x x
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