傅里叶系数求解公式的推广

Generalization of Fourier Coefficients Formula

针对教材中傅里叶系数公式在具体应用过程中有时需要对函数进行平移的不便之处,给出了求解傅里叶系数公式的一个推广形式,并进行了证明,同时把推广公式应用到具体实例中,得到了一致的结果.推广公式在应用过程中更加简便、实用.

This paper presents a generalization form of Fourier coefficients formula because of the inconvenience of function shift to derive the Fourier coefficients in the textbook. We prove the generalization form and also apply it to some specific instances. The results are the same as those of the conventional Fourier coefficients. The generalization form is more convenient and practicable.