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Izolovana osobliva tochka z 0 displaystyle z 0 nazivayetsya polyusom funkciyi f z displaystyle f z yaksho v rozkladanni ciyeyi funkciyi v ryad Lorana v prokolotomu okoli tochki z 0 displaystyle z 0 golovna chastina mistit skinchene chislo vidminnih vid nulya chleniv tobtoGrafik pokazuye absolyutnu velichinu gamma funkciyi Vidno sho funkciya staye neskinchenoyu v polyusah livoruch Pravoruch gamma funkciya ne maye polyusiv vona prosto shvidko zrostaye f z k f k z z 0 k P z f n z z 0 n f 1 z z 0 1 displaystyle f z sum k infty infty f k z z 0 k P z f n z z 0 n ldots f 1 z z 0 1 de P z displaystyle P z pravilna chastina ryadu Lorana Yaksho f n 0 displaystyle f n neq 0 to z 0 displaystyle z 0 nazivayetsya polyusom poryadku n displaystyle n Yaksho n 1 displaystyle n 1 to polyus nazivayetsya prostim Kriteriyi viznachennya polyusa RedaguvatiTochka z 0 displaystyle z 0 nbsp ye polyusom todi i tilki todi koli lim z z 0 f z displaystyle lim z to z 0 f z infty nbsp Tochka z 0 displaystyle z 0 nbsp ye polyusom poryadku k displaystyle k nbsp todi i tilki todi koli lim z z 0 f z z z 0 k 1 displaystyle lim z to z 0 f z z z 0 k 1 infty nbsp a lim z z 0 f z z z 0 k displaystyle lim z to z 0 f z z z 0 k neq infty nbsp Tochka z 0 displaystyle z 0 nbsp ye polyusom poryadku k displaystyle k nbsp todi i tilki todi koli vona ye dlya funkciyi F z 1 f z displaystyle F z frac 1 f z nbsp nulem poryadku k displaystyle k nbsp Divis takozh RedaguvatiNul kompleksnij analiz Otrimano z https uk wikipedia org w index php title Polyus kompleksnij analiz amp oldid 12266755