golomorf funksiyalarning xossalari

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1526023809_71483.doc () fz d ) ( z c d ì () fz d g ( ) 0 fzdz g = ò ()() fzd îj ( ) z dc ì d d z î " ò ¶ - = d d z f z f x x x p ) ( i 2 1 ) ( ()() fzd îj ( ) z dc ì () fz d x x x p g d z f n z f n n ò + - = 1 ) ( ) ( i 2 ! ) ( ( ) 1,2,3... n = d - g g ò - = g x x x p d z f z f ) ( i 2 1 ) ( ) ( z f ò ò = - - d - - = d + g g x x x p x x x p d z f …

òò ( ) ( ) c z f j î ( ) z f c ( ) z f r < - | | a z za - ( ) ( ) 0 , n n n fzcza ¥ = =- å ( ) ( ) ò + - = g x x p d a z f i c n n 1 2 1 ( ) m z f £ | | ( ) ( ) c z f j î r ,... 3 , 2 , 1 = n ,..) 3 , 2 , 1 ( 0 lim = = m ¥ ® n n r r r ,... 3 , 2 , 1 = n 0 = n c ,... 3 , 2 , 1 = n c ( ) ( ) const c c z f = = 0 0 ( ) z f d z …

bo’ladi. natija 2. agar funksiya sohada boshlang’ich funksiyaga ega bo’lsa, u holda sohada golomorf bo’ladi. funksiyani teylor qatoriga yoyish. agar bo’lsa, u holda nuqtada (a nuqtaning atrofida) teylor qatoriga yoyiladi: isbot. ning chegarasini deylik. bo’ladi. avvalo funksiyani quyidagicha yozib, so’ng bo’lishini e’tiborga olib topamiz: . (6) bu geometrik qator bo’lib, uning maxraji ga teng. ravshanki, uchun quyidagi tengsizlik o’rinli. demak, (4) qator yaqinlashuvchi. (6) tenglikning har ikki tomonini ga ko`paytirib, so’ng chiziq bo’yicha integrallab, ushbu tenglikka kelamiz. (5) va (6) munosabatlardan bo’lishi kelib chiqadi. integral ostidagi qatorning hadlari uchun tengsizlik o’rinli bo’ladi. ravshanki, qator yaqinlashuvchi. unda veyershtrass alomatiga ko’ra funktsional qator da tekis yaqinlashuvchi bo’ladi. binobarin, bu qatorni hadlab integrallash mumkin. unda (7) tenglik ushbu ko’rinishga keladi. yuqorida keltirilgan ma’lum teoremaga ko’ra bo’lishini topamiz. natijada (8) va (9) tengliklardan bo’lishi kelib chiqadi. bu esa funksiyani teylor qatoriga yoyilganini bildiradi. natija 3. agar funksiya yopiq doirada golomorf bo’lib, bu doiraning chegarasi …

piq chiziq bo’lsin. agar bo’lsa, u holda funksiya sohada golomorf bo’ladi. isbot. teoremada keltirilgan shart bajarilganda funksiya sohada boshlang’ich funksiyaga ega bo’lib, funksiya da differensiallanuvchi, ya’ni golomorf bo’ladi. 30-xossaning 1-natijasiga ko’ra ham sohada golomorf bo’ladi. ayni paytda bo’lganligi sababli bo’ladi. 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. _1175013839.unknown _1175150267.unknown _1441534790.unknown _1441535419.unknown _1441537490.unknown _1441537864.unknown _1441538780.unknown _1441538997.unknown _1441539032.unknown _1441538404.unknown _1441537600.unknown _1441535709.unknown _1441537245.unknown _1441535602.unknown _1441535076.unknown _1441535307.unknown _1441535331.unknown _1441535204.unknown _1441534922.unknown _1441535009.unknown _1441534800.unknown _1176302184.unknown _1176303770.unknown _1176303797.unknown _1176303849.unknown _1176303884.unknown _1176303924.unknown _1176303943.unknown _1176303904.unknown _1176303861.unknown _1176303821.unknown _1176303785.unknown _1176303593.unknown _1176303732.unknown _1176303741.unknown _1176303722.unknown _1176303542.unknown _1176303579.unknown _1176303435.unknown _1176303373.unknown _1176303387.unknown _1176302270.unknown _1176302060.unknown _1176302084.unknown …

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1526023809_71483.doc () fz d ) ( z c d ì () fz d g ( ) 0 fzdz g = ò ()() fzd îj ( ) z dc ì d d z î " ò ¶ - = d d z f z f x x x p ) ( i 2 1 ) ( ()() fzd îj ( ) z dc ì () fz d x x x p g d z f n z f n n ò + - = 1 ) ( ) ( i 2 ! ) ( ( ) 1,2,3... n = d - g g ò - = g x x x p d z f z f ) ( i 2 1 …

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