Prove that
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Originally Posted by simplependulum Prove that changing to in gives us: call this (1). we also have call this (2). multiply (1) by (2) to get: call this (3). now equating the coefficients of in both sides of (3) gives us: and the result follows.
Let's start with the Fourier Series (It may also be done in other ways, see ): - integrating again- Repeating the process we get: for Now set: Here
Excellent ! I couldn't imgaine that there is one more solution for this question .
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