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How to find the sum $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots =\ ?$

Can I make this deduction involving inner product, discrete/continuous convolution and Fourier transform?

$L^p$ norm of Dirichlet Kernel

Fourier transform of $1/|x|^{\alpha}$.

Prove Parseval for the Fourier transform

Estimate the integral of the absolute value of the Dirichlet kernel

Orthonormal system for $L^2(\mathbb R)$

Evaluate $\int_{0}^{\infty}\dfrac{\mathrm dx}{(e^{\pi x}+e^{-\pi x})(16+x^2)}$

Smoothness and decay property of Fourier transformation

Does band-limited imply continuous?

Why this function can't be used in Fourier expansion?

Difficulty in understanding a part in a proof from Stein and Shakarchi Fourier Analysis book.

Regularizing effect of the heat equation

Decay of amplitude integral

Are Fourier series a basis for $L^2((-\pi,\pi)^m)$?

Show that f is a polynomial

Creating intuition about Laplace & Fourier transforms

New posts in fourier-analysis

How to find the sum $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots =\ ?$

A positive "Fourier transform" is integrable

A funtion and its fourier transformation cannot both be compactly supported unless f=0 [duplicate]

How to calculate the Fourier Transform of a constant?

Can I make this deduction involving inner product, discrete/continuous convolution and Fourier transform?

$L^p$ norm of Dirichlet Kernel

Fourier transform of $1/|x|^{\alpha}$.

Prove Parseval for the Fourier transform

Estimate the integral of the absolute value of the Dirichlet kernel

Orthonormal system for $L^2(\mathbb R)$

Evaluate $\int_{0}^{\infty}\dfrac{\mathrm dx}{(e^{\pi x}+e^{-\pi x})(16+x^2)}$

Smoothness and decay property of Fourier transformation

Does band-limited imply continuous?

Why this function can't be used in Fourier expansion?

Difficulty in understanding a part in a proof from Stein and Shakarchi Fourier Analysis book.

Regularizing effect of the heat equation

Decay of amplitude integral

Are Fourier series a basis for $L^2((-\pi,\pi)^m)$?

Show that f is a polynomial

Creating intuition about Laplace & Fourier transforms