مرحبا بالجميع
أنا أطلب منك أن تساعدني في حل السؤال التالي:
س: العثور على سلسلة فورييه وظيفة فترة و ( س ) = ه - | س | ، - 1 ≤ س ≤ 1.
Google suggests:Now, I suppose that the function is suppose to be $f(x) = \mathrm e^{|x|}$ in the interval $[-1, 1]$.Hello Paljmaaona ask you to help me in solving the following question: Q: Finding a Fourier series and the function f (x) = e - | x |, - 1 ≤ x ≤ 1.
The first thing to notice is that this is an even function. Therefore it's Fourier Series will be a Cosine series $${a_0 \over 2} + \sum_{n=1}^\infty a_n\cos {(\pi n x)}$$
where the $a_n$ are given by$$\int_{-1}^1 \mathrm e^{|x|}\cos {(\pi n x)} \, \mathrm d x$$
But because these are even functions we know that$$\int_{-1}^1 \mathrm e^{|x|}\cos {(\pi n x)} \, \mathrm d x = 2\int_0^1 \mathrm e^{x}\cos {(\pi n x)} \, \mathrm d x$$
Can you proceed from here?