Question

Evaluate $\int_{-\pi}^\pi \big|\sum^\infty_{n=1} \frac{1}{2^n} e^{inx}\big|^2 \operatorname d\!x$

score 296 · Answer 1 · 2026-04-17 00:32:52

296

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Evaluate $\int_{-\pi}^\pi \big|\sum^\infty_{n=1} \frac{1}{2^n} e^{inx}\big|^2 \operatorname d\!x$

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5.6k

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105

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201

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score 370 · Answer 7 · 2026-04-08 18:11:50

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417

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511

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score 223 · Answer 12 · 2026-04-13 16:34:39

223

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564

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300

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List Question

Evaluate $\int_{-\pi}^\pi \big|\sum^\infty_{n=1} \frac{1}{2^n} e^{inx}\big|^2 \operatorname d\!x$

What is the advantage of using Fourier Series representation rather than the function itself?

Is continuous function space with standard inner product on $\big[0,\frac{1}{2}\big]$ not complete?

An $L^1$ function whose Fourier series converges but not to itself

Phase speed of 2D wave

How to make sense of Fourier series for a distribution?

Solving the heat equation using Fourier series; specific questions

Fourier Series of a decaying Cosine

Why should we use the Fourier Transform?

Big O proof of Fourier Coefficient

2-D Fourier Transform of complex exponential with 2-D quadratic phase

How to get Fourier–Stieltjes transform on $\mathbb R$ from the nice function on $\mathbb T$ (periodic on $\mathbb R$)?

Fourier series/transform with cutoff

Fourier transform real and imaginary part question?

Heat equation. Find $B_n$ (using boundary conditions?)

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