फलन अनुक्रम {sin(mx)}, m = 1, 2, ... अंतराल [-π, π] पर एक लांबिक (orthogonal) निकाय बनाता है। जब m ≠ n हो, तो समाकल ∫-ππ sin(mx) sin(nx) dx का मान क्या है?

For the function f(x) = x2 defined on -π ≤ x ≤ π, if its Fourier series expansion is f(x) = a02 + ∑n=1∞ (an cos(nx) + bn sin(nx)), then the values of the Fourier coefficients a0, an, and bn are:

In the Fourier series expansion of a periodic function f(x) over an interval of length 2K (period T = 2K), which term correctly represents the argument of the trigonometric functions?