loran qatori

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$1525843796_71454.doc ( ) z f 0, rr ³£+¥ { } : z vzcrzar =î ' , ' ( ) ( ) ' fzv îj ' v z î " ( ) ( ) ò ¶ - = ' 2 1 v d z f i z f x x x p ''' v г ¶=g u ( ) ( ) ( ) ( ) ''' 111 222 v г fff fzddd iziziz ¶g xxx =x=x-x px-px-px- òòò { } { } '','' гarar =x-=g=x-= ' г "xî 1 za a æö - r r ³ rr £ ( ) n n n cza ¥ =-¥ - å { } :|| z zcrzar î 2 1111 1...... n zzzz æö -+++++ ç÷ èø 1 11 1 n n zz ¥ = = - å { } 1 z > { } 12 vz =<< ( ) 0110 1 22 nn n …$

i bo’lishini topamiz. bu hol va yig’indilarni birlashtirib, ushbu ko’rinishda yozish imkonini beradi: . demak, bo’lib, bunda bo’ladi. ta’rif. koeffitsientlari (2) formula bilan aniqlangan (1) qator funksiyaning sohadagi (halqadagi) loran qatori deyiladi. funksiya sohada (halqada) golomorf bo’lsa, teoremaga binoan bo’lishini e’tiborga olib, bu holda funksiya sohada (halqada) loran qatoriga yoyiladi deb aytamiz. ushbu (10) qatorga loran qatorining to’g’ri qismi, (11) qatorga esa loran qatorining bosh qismi deyiladi. loran qatorining to’g’ri qismi darajali qatordir. uning yaqinlashish sohasi abel teoremasiga ko’ra doiradan iborat bo’lib, yaqinlashish radiusi koshi–adamar formulasi ga ko’ra topiladi. (10) qator da tekis yaqinlashuvchi bo’ladi. loran qatorini bosh qismi da o’zgartirish kiritsak, unda ko’rinishga keladi. bu qator abel teoremasiga ko’ra da yaqinlashadi, yaqinlashish radiusi koshi –adamar formulasiga ko’ra bo’ladi. demak, qator doiraning tashqi qism bo’lgan sohada yaqinlashuvchi bo’ladi. agar bo’lsa, loran qatorini yaqinlashish sohasi bo’sh to’plamdan iborat bo’ladi. agar bo’lsa, loran qatori ning yaqinlashish sohasi halqadan iborat bo’ladi. bo’lsa, bitta …

gidan doirada golomorf. ravshanki, bo’lib, bo’ladi. demak, . bu qator doirada yaqinlashuvchi. endi o’ng tomondagi funksiyani olib, uni quyidagicha yozib olamiz: . bu funksiya da golomorf bo’lib, u yaqinlashuvchi qatorga yoyiladi. demak, bo’lib, u da yaqinlashuvchi bo’ladi. natijada sohada (15) tenglikka ko’ra bo’ladi. demak, . adabiyоtlar: 1. шабат б.в. введение в комплексный анализ. 2-nashri, 1-ч.-м, “наука”, 1976. 2. xudoyberganov g., vorisov a., mansurov x. kompleks analiz. (ma’ruzalar). t, “universitet”,1998. 3. sadullaev a., xudoybergangov g., mansurov x., vorisov a., tuychiev t. matematik analiz kursidan misol va masalalar to’plami. 3-qism (kompleks analiz) “o’zbekiston”,2000. 4. волковыский л.и., лунц г.л., араманович и.г. сборник задач по теории функций комплексного переменного. 3- nashri. – м. “наука”, 1975. _1441559997.unknown _1441603756.unknown _1441609872.unknown _1441610949.unknown _1441612382.unknown _1441612607.unknown _1441613005.unknown _1441613338.unknown _1441613499.unknown _1441613018.unknown _1441612742.unknown _1441612543.unknown _1441612023.unknown _1441612187.unknown _1441612291.unknown _1441612098.unknown _1441611897.unknown _1441611923.unknown _1441611462.unknown _1441610318.unknown _1441610703.unknown _1441610885.unknown _1441610507.unknown _1441610198.unknown _1441610243.unknown _1441610078.unknown _1441607951.unknown _1441608629.unknown _1441609750.unknown _1441609792.unknown _1441609368.unknown _1441608503.unknown _1441608573.unknown _1441608142.unknown _1441607671.unknown _1441607702.unknown _1441607793.unknown _1441603771.unknown _1441607398.unknown …

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1525843796_71454.doc ( ) z f 0, rr ³£+¥ { } : z vzcrzar =î ' , ' ( ) ( ) ' fzv îj ' v z î " ( ) ( ) ò ¶ - = ' 2 1 v d z f i z f x x x p ''' v г ¶=g u ( ) ( ) ( ) ( ) ''' 111 222 v г fff fzddd iziziz ¶g xxx =x=x-x px-px-px- òòò { } { } '','' гarar =x-=g=x-= ' г "xî 1 za a æö - r r ³ rr £ ( ) n n n cza ¥ =-¥ - å { } :|| z zcrzar î 2 1111 1...... n zzzz æö -+++++ …

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