Koj ua li cas lub zog series expansion?
Koj ua li cas lub zog series expansion?

Video: Koj ua li cas lub zog series expansion?

Video: Koj ua li cas lub zog series expansion?
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Fais fab Series Expansions . Rn=f(n+1)(ξ)(x−a)n+1(n+1)!, a<ξ<x. Yog qhov no nthuav dav converges dhau ib yam ntawm x centered ntawm a, uas yog, limn → ∞Rn = 0, ces tus nthuav dav hu ua Taylor series ntawm qhov ua haujlwm f(x) nthuav dav txog lub ntsiab lus a.

Hauv qhov no, dab tsi yog qhov txiaj ntsig ntawm lub hwj chim series?

(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.

Tsis tas li ntawd, Power series siv rau dab tsi? 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.

Ntawm no, muaj peev xwm muaj peev xwm sawv cev raws li lub hwj chim series?

3 Teb. A muaj peev xwm ua sawv cev raws li lub hwj chim series yog hais tias thiab tsuas yog hais tias nws yog complex txawv nyob rau hauv ib tug qhib teeb. 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.

Dab tsi yog lub vojvoog ntawm convergence ntawm lub hwj chim series?

Radius ntawm convergence . Los ntawm Wikipedia, dawb encyclopedia. Hauv lej, the Lub vojvoog ntawm convergence ntawm lub hwj chim series yog cov lub vojvoog ntawm qhov loj tshaj plaws disk uas lub series converges . Nws yog tus lej tiag tiag lossis tsis zoo..

Pom zoo: