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Jiaxin Zhong
  • Member for 5 years
  • Last seen more than a week ago
527 votes
27 answers
195k views

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

  • 8,739
29 votes
1 answer
867 views

Prove that $ \sum\limits_{n=-\infty}^\infty\frac{\cos\pi\sqrt{n^2+1}}{3+4n^2}=\int\limits_{-\infty}^\infty\frac{\cos\pi\sqrt{x^2+1}}{3+4x^2}dx $?

28 votes
1 answer
4k views

"Sum equals integral" identities similar to $\int_0^1 \frac{dx}{x^x} = \sum_{n = 1}^{\infty} \frac{1}{n^n}$

  • 3,352
19 votes
2 answers
7k views

Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?

  • 820
15 votes
4 answers
987 views

Does there exist a closed form for the sinc function series $\sum_{n=1}^\infty \frac{\sin\sqrt{n^2+1}}{\sqrt{n^2+1}}$?

3 votes
1 answer
174 views

How to derive the Taylor's theorem logically?

1 vote
2 answers
185 views

Does there exist a closed form for the non-integer shifted sinc-function series: $\frac{\sin(n+a)x}{(n+a)x}$?

0 votes
1 answer
185 views

Integral over triple Legendre polynomials involving derivatives