vishak h pillai

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An Engineer turned student of Theoretical Mathematics.

Love Abstract Sciences and just love this site.

A Theoretical Research Mathematician one day .

28 Questions

 5 Prove that the zeros of an analytic function are finite and isolated 3 $\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent? 3 $\int_{0}^{\infty} f(x) \,dx$ exists. Then $\lim_{x\rightarrow \infty} f(x)$ must exist and is $0$. A rigorous proof? 3 Is the Series : $\sum_{n=1}^{\infty} \left( \frac 1 {(n+1)^2} + …+\frac 1 {(n+n)^2} \right) \sin^2 n\theta$ convergent? 2 $\lim_{n\rightarrow \infty}\int_{x=a}^{x=b} f_n(x) dx = \int_{x=a}^{x=b} f(x) dx$ only when f is uniformly convergent?

318 Reputation

 +15 $\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent? +10 Is the function $f(x)= {\sin x \over x}$ uniformly continuous over $\mathbb{R}$? +18 $\int_{0}^{\infty} f(x) \,dx$ exists. Then $\lim_{x\rightarrow \infty} f(x)$ must exist and is $0$. A rigorous proof? +5 $\lim_{n\rightarrow \infty}\int_{x=a}^{x=b} f_n(x) dx = \int_{x=a}^{x=b} f(x) dx$ only when f is uniformly convergent?

 1 Is the function $f(x)= {\sin x \over x}$ uniformly continuous over $\mathbb{R}$? 1 The proof of Raabe's Test for absolute convergence 0 Prove that a cyclic group can have no more than one element of order two. 0 Proof on equivalence relations help 0 Groups Math Proof Help

25 Tags

 1 real-analysis × 9 0 complex-numbers × 4 1 uniform-continuity 0 elementary-number-theory × 3 0 matrices × 8 0 group-theory × 3 0 abstract-algebra × 6 0 block-matrices × 3 0 complex-analysis × 4 0 integration

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