Bamily

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11 Questions

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6	Show $ \int_{-\pi}^{\pi} \frac{1 - \cos (n+1) x}{1- \cos x} dx = (n+1) 2 \pi$ for $n \in \mathbb N$ [duplicate]
4	Show $1 + 2 \sum_{n=1}^N \cos n x = \frac{ \sin (N + 1/2) x }{\sin \frac{x}{2}}$ for $x \neq 0$
3	How can I prove $\lim_{n \to \infty} \int_{0}^{\pi/2} f(x) \sin ((2n+1) x) dx =0 $?
2	About completeness of the Fourier series.
2	A simple question about the open mapping theorem

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132 Reputation

+1	When does $\\| f^2 \\|_2 \leqslant c \\| f \\|_2 $ hold?
+10	Show $ \int_{-\pi}^{\pi} \frac{1 - \cos (n+1) x}{1- \cos x} dx = (n+1) 2 \pi$ for $n \in \mathbb N$
+5	A simple question about the open mapping theorem
+5	Show $1 + 2 \sum_{n=1}^N \cos n x = \frac{ \sin (N + 1/2) x }{\sin \frac{x}{2}}$ for $x \neq 0$

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0 Answers

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16 Tags

0 functional-analysis × 4	0 vector-spaces
0 fourier-analysis × 3	0 operator-theory
0 real-analysis × 2	0 banach-spaces
0 calculus × 2	0 fourier-series
0 linear-algebra	0 differential-equations

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$Mathematics Stack Exchange$

Mathematics

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