Furye qatori. Funksiyalarni Furye qatoriga yoyish
Maxsud Tulqin o’g’li Usmonov
maqsudu32@gmail.com
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
maqsudu32@gmail.com
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
"Science and Education" Scientific Journal / Impact Factor 3.848 (SJIF)
January 2023 / Volume 4 Issue 1
www.openscience.uz / ISSN 2181-0842
77