Power series siv rau dab tsi?
Power series siv rau dab tsi?

Video: Power series siv rau dab tsi?

Video: Power series siv rau dab tsi?
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Lub zog series expansions yuav ua tau siv kom kwv yees qhov tseem ceeb ntawm cov ntsiab lus tseeb, thiab ib qho piv txwv yog qhov yuam kev integral (kev sib koom ua ke yog e-x2) vim qhov no ua rau muaj kev hloov pauv. series (txawm tias x yog qhov tsis zoo), thiab yog li qhov yuam kev tuaj yeem kwv yees tau yooj yim.

Dhau li ntawm no, vim li cas peb thiaj siv lub hwj chim series?

1 Teb. Tej zaum qhov tseem ceeb tshaj plaws yog vim li cas lub zog series muaj txiaj ntsig yog tias lawv tso cai rau koj los kwv yees ib qho (tejzaum nws convoluted, tab sis du) muaj nuj nqi f(x) los ntawm nws (txiav) lub zog series f(x)=∑nanxn=∑n≦Nanxn+O(xn+1).

Ib yam li ntawd, series siv rau dab tsi? Series yog siv hauv feem ntau ntawm kev ua lej, txawm tias kawm txog cov qauv finite (xws li hauv combinatorics), los ntawm kev tsim cov haujlwm. Ntxiv nrog rau lawv cov ubiquity nyob rau hauv lej, infinite series kuj dav siv hauv lwm yam kev qhuab qhia xws li physics, computer science, kev txheeb cais thiab nyiaj txiag.

Ib yam li ntawd, lub hwj chim series txhais tau li cas?

(x-a)n. Seb tus series converges los yog diverges, thiab tus nqi nws converges rau, nyob ntawm seb tus x-tus nqi, uas ua rau lub zog series ib function.

Puas muaj peev xwm sawv cev ua lub hwj chim series?

3 Teb. A muaj peev xwm ua sawv cev raws li lub hwj chim series yog tias thiab tsuas yog nws yog qhov sib txawv ntawm qhov sib txawv hauv qhov qhib. Qhov no ua raws los ntawm daim ntawv dav dav ntawm Taylor's theorem rau complex muaj nuj nqi . Yog vim li cas yog qhov complexified version ntawm lub muaj nuj nqi tsis tas li ntawm lub hauv paus chiv keeb.

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