kompleks o’zgaruvchili funksiyaning integrali va uning xossalari koshi teoremasi

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silliq) yopiq egri chiziq bo’lsin. integralning 6-xossasiga ko’ra d sohaga tegishli bo’lgan shunday p ko’pburchak topiladiki, bo’ladi, bunda ixtiyoriy musbat son 2) holga binoan demak, bundan esa bo’lishi kelib chiqadi. teorema to’liq isbot bo’ldi. natija 1. agar f(z) funksiya bir bog’lamli d sohada golomorf bo’lsa, u holda f(z) funksiyaning integrali integrallash egri chizig’iga bog’liq bo’lmaydi, ya’ni boshlang’ich va oxirgi nuqtalari umumiy hamda d sohada yotuvchi va egri chiziqlar uchun bo’ladi. 2. koshi teoremasini umumlashtirish. aytaylik, d chegarlangan bir bog’lamli soha bo’lib, uning chegarasi silliq (bo’lakli silliq) yopiq egri chiziqdan iborat bo’lsin. teorema: agar bo’lsa, u holda bo’ladi. bu erda ni yo’nalishi musbat yo’nalish. soha berilgan bo’lsin. d soha chegarasi ni orientirlangan yo’nalish deb shunday yo’nalishga aytiladiki, bu yo’nalish bo’yicha chegarada harakat qilganda soha har doim chap tomonda qoladi. teorema: (ko’p bog’lamli soha uchun koshi teoremasi) agar f(z) funksiya ko’p bog’lamli d sohada golomorf va da uzluksiz bo’lsa, u holda bo’ladi. …

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1526023587_71479.doc n g g g ,... , 2 1 k g l k n k l £ £ = 1 max l k x ) ( k f x 1 - - k k z z ( ) ( ) å = - - = n k k k k z z f 1 1 x s k x 0 ® l g k g k x g ( ) ò g dz z f ( ) ( ) ( ) å ò = - ® - = n k k k k z z f dz z f 1 1 0 lim x l g g ( ) c ab î = g g ( ) ( ) ( …

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