Ред на фурие

[Гост]

Функцията y=2[tex]x^{2 }[/tex]-x
x e (-[tex]\pi, \pi[/tex]) период 2[tex]\pi[/tex] Да се развие в ред на фурие

[KOPMOPAH]

Период$$T = 2 \pi$$Честота $$\omega = \frac{2 \pi}{T}$$ $$\omega = 1$$ $$a = - \pi$$ $$b = \pi$$

$$a_{0} + \sum_{K=1}^{\infty} \left(a_{n} \cos{\left(K \omega x \right)} + b_{n} \sin{\left(K \omega x \right)}\right)$$
$$a_{0} = \frac{\int\limits_{- \pi}^{\pi} f{\left(x \right)}\, dx}{T}$$
$$a_{0} = \frac{\int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right)\, dx}{2 \pi}$$
$$a_{n} = \frac{2 \int\limits_{a}^{b} f{\left(x \right)} \cos{\left(K \omega x \right)}\, dx}{T}$$
$$a_{n} = \frac{2}{2 \pi} \int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right) \cos{\left(K x \right)}\, dx$$
$$b_{n} = \frac{2 \int\limits_{a}^{b} f{\left(x \right)} \sin{\left(K \omega x \right)}\, dx}{T}$$
$$b_{n} = \frac{2}{2 \pi} \int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right) \sin{\left(K x \right)}\, dx$$
$$K = 1, 2, 3, ..$$
$$\sum_{K=1}^{\infty} \left(2 \frac{1}{2 \pi} \sin{\left(K x \right)} \int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right) \sin{\left(K x \right)}\, dx + 2 \frac{1}{2 \pi} \cos{\left(K x \right)} \int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right) \cos{\left(K x \right)}\, dx\right) + \frac{\int\limits_{- \pi}^{\pi} \left(2 x^{2} - x\right)\, dx}{2 \pi}$$

[Гост]

Благодаря

[Гост]

kakvo znachi furie spored teb?