Evaluation of the constants in Fouriers series

Assuming Fourier s series to be valid between the limits x = + 7r and x = - 7r, we shall now proceed to find values for the coefficients A0, av a2. bv b2. which will make the series true. 

To find a value for the constant A0. Multiply equation (1) by dx and then integrate each term between the limits x = + tr and x = - 7r. Every term involving sine or cosine term vanishes, and 

I strongly recommend the student to master 74, 75, 83 before taking up this chapter. 

IL To find a value for the coefficients of the cosine terms, say hn, where n may b9 any number from 1 to n. Equation (1) must not only be multiplied by dx, but also by some factor such that all the other terms will vanish when the series is integrated between the limits + tt, bncos nx remains. Such a factor is cos nx. dx. In this case, 

This formula enables any coefficient, bv b2,. .., bn to be obtained. If we put n = 0, the coefficient of the first term A0 assumes the form, 

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