Science and Education

"Science and Education" Scientific Journal / Impact Factor 3.848 (SJIF)

January 2023 / Volume 4 Issue 1

_{Furye qatori. Funksiyalarni Furye qatoriga yoyish}

Maxsud Tulqin o’g’li Usmonov [e-mail]

Mirzo Ulug‘bek nomidagi O‘zbekiston Milliy universiteti


Annotatsiya: Ushbu maqolada matematikaning eng muhim mavzularidan biri bo’lgan Furye qatori. Funksiyani Furye qatoriga yoyish tog’risida malumot keltirildi va mavjud muanmolar xal etildi. Agar f (x) funksiya [a;b] kesmada monoton bo‘lsa yoki [a;b] kesmani chekli sondagi qismiy kesmalarga bo‘lish mumkin bo‘lsa va bu kesmalarning har birida f (x) funksiya monoton (faqat o‘ssa yoki faqat kamaysa) yoki o‘zgarmas bo‘lsa, f (x) funksiyaga [a;b] kesmada bo‘laklimonoton funksiya deyiladi. Agar f (x) funksiya [a;b] kesmada chekli sondagi birinchi tur uzilish nuqtalariga ega bo‘lsa, f (x) funksiyaga [a;b] kesmada bo‘lakli-uzluksiz funksiya deyiladi. Agar f (x) funksiya [a;b] kesmada uzluksiz yoki bo‘lakli-uzluksiz bo‘lib, bo‘lakli-monoton bo‘lsa f (x) funksiya [a;b] kesmada Dirixle shartlarini qanoatlantiradi deyiladi. Bu hоllаrdа qo’yilgаn mаsаlаlаrni yеchishdа quyidа biz o’rgаnаdigаn qаtоrlаr nаzаriyasi kаttа аhаmiyatgа egа.
Kalit so’zlar: Furye qatori, Furye koeffitsiyentlari. Funksiyalarni Furye qatoriga yoyish.


Fourier series. Fourier series expansion of functions

Maxsud Tulqin oglu Usmonov [e-mail]

National University of Uzbekistan named after Mirzo Ulugbek


Abstract: In this article, the Fourier series is one of the most important topics in mathematics. Information on the expansion of the function into the Fourier series was given and the existing problems were solved. If the function f (x) is monotone in the section [a;b] or if the section [a;b] can be divided into a finite number of partial sections, and in each of these sections the function f (x) is monotone (only if or only decreases) or is constant, the function f (x) is called a piecewise monotone function on the cross section [a;b]. If the function f (x) has a finite number of discontinuities of the first type on the section [a;b], then the function f (x) is called a piecewise- continuous function on the section [a;b]. If the function f (x) is continuous or piecewise-continuous in the cross section [a;b], and is piecewise monotone, then the function f (x) is said to satisfy the Dirichlet conditions in the cross section [a;b]. The

theory of series, which we will study below, is of great importance in solving the problems posed in these cases.