Consider the function f$($x$)=$e$^(2$x$)$ defined on the interval a$\_(0),$a$\_($n$),$b$\_($n$)$f$($x$)=$a$\_(0)+\backslash$sum$\_($n$=1)^(\backslash$infty $)$ a$\_($n$)$cosnx$+$b$\_($n$)$sinnx$.$a$\_(0)=(1)/(2\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$dx$,$a$\_($n$)=(1)/(\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$cosnxdx$,$b$\_($n$)=(1)/(\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$sinnxdx$.-\backslash$pi $.$ Calculate

the coefficients a$\_(0),$a$\_($n$),$b$\_($n$)$ for the Fourier series

f$($x$)=$a$\_(0)+\backslash$sum$\_($n$=1)^(\backslash$infty $)$ a$\_($n$)$cosnx$+$b$\_($n$)$sinnx$.$

Reminder:

a$\_(0)=(1)/(2\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$dx$,$a$\_($n$)=(1)/(\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$cosnxdx$,$b$\_($n$)=(1)/(\backslash$pi $)\backslash$int$\_(-\backslash$pi $)^(\backslash$pi $)$ f$($x$)$sinnxdx$.$