Question

write the complex form of fourier series?​

Answer 1

Answer:

we can write the Fourier series of the function in complex form: f(x)=a02+∞∑n=1(ancosnx+bnsinnx)=a02+∞∑n=1(aneinx+e−inx2+bneinx−e−inx2i)=a02+∞∑n=1an−ibn2einx+∞∑n=1an+ibn2e−inx=∞∑n=−∞cneinx. Here we have used the following notations: c0=a02,cn=an−ibn2,c−n=an+ibn2.

Explanation:

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