powerseriesexpansionanditsapplications-外文文獻(xiàn)-全文預(yù)覽
【正文】 epowerseris21 112! !nxx xn++++… … , (956)Obviously,(956)typeconvergenceinterval(,)?∞+,As(956)whetrtype()xfxe=isSumfunction,thatis,whetritconvergesto()xfxe=,butalsoexam inerem ainder ()1e()(1)!xnnrx xnθ +=+(01θ)， 且 xxxθθ≤≤,Therfore209NO .8O O OPrincipleofmathematicalnalysi211 1e e()(1)! (1)!xx n nnrx x xn nθ + += + +,Notingthevalueofanysetx,xeisafixedconstant,whilethesries(956)isabsolutelyconvergent,sothegneralwhentheitem when→∞, 1 0(1)!nxn+→+,sowhen→∞,ther 1 0(1)!nxxen+→+,From thislim ()0nnrx→∞=Thisindicatesthathesries(956)doesconvergeto()xfxe=,therfore21 112! !x nexx xn=++++… … ( x?∞+∞).SuchuseofMaclurinform ulaarexpadeinpowerserism ethod,althoughteprocedureisclear,butoperatorsareoftentoCum bersom e, soitisgenralym oreconvenitousethefolwingpowerserisexpansionm ethod.Priortothis,wehavebenafunctionx?11,xeandsinxpowerserisexpansion,theuseofthesknownexpansionbypowerserisofperations,wecanchievm andfunctionfpoerserisexpansionm ple2Findthefunction()cosfxx=, 0=,Departm enti
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