powerseriesexpansionanditsapplications-外文文獻(文件)
【正文】 xn n∞= ′=+++ +∑ … … .(954)Itisthefunction()fxthepowerserisexpresion,if,asum ingthefunctionf(x)canbexpresdaspowerseris209NO .8O O OPrincipleofmathematicalnalysi21020200() n nn nnfxaxaaxaxax∞= =+++++∑ … … , (95)Wel,acordingtotheconvergenceofpowerseriscanbeitem izdwithinthenatureofderivation,andthenm ake 0x=(powerserisaparentlyconvergesinthe0x=point),itiseasytoget()20 1 2 (0) 0)(0), (0), , ,2! !n nnf fafafxa xa xn′′== = =… … .Substiutingthem into(95)type,in eand()fxtheMaclurinexpansionf(954) m ary, ifthefunctionf(x)containszeroinarngeofarbitrayorderderivative,andinthisrangeofMaclurinform ulaintherm aindertozeroasthelim t(when→∞,)then,thefunctionf(x)canstartform ingas(954) ()20 0 00 0 0 0() () )()() ( ) ( ) ( )1! 2! !n nfx fx fxfxfx xx xx xxn′ ′=+ ?+ ?++ ?… … ,prim aryfunctionfpowerserisexpansionMaclurinform ulausingthefunction()fxexpandeinpowerserism ethod,caledthedirectexpansionm ple1Testhefunction()xfxe=())n xfxe=,(1,2,3,)n=…Therfore ()(0)(0)(0)0)1nf f f f′ ′=== =… ,Sowegth
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