Question

Maclaurin series of G(x)=$ \int_{0}^{x} \frac{1-e^{-y^2}}{y^2} \ dy $

score 37 · Answer 1 · 2019-11-16 17:04:34

37

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Maclaurin series of G(x)=$ \int_{0}^{x} \frac{1-e^{-y^2}}{y^2} \ dy $

Published on 16 Nov 2019 - 17:04

score 45 · Answer 2 · 2026-02-23 21:31:19

45

Views

Uniform/Pointwise Convergence

Published on 23 Feb 2026 - 21:31

score 64 · Answer 3 · 2019-11-17 20:48:02

64

Views

Proving the uniform convergence of $ f_n (x) = \sin(\frac{1}{n})\cos(x)$

Published on 17 Nov 2019 - 20:48

score 36 · Answer 4 · 2019-11-18 01:55:34

36

Views

Does $f_n(x) = \sum_{k=0}^n x^k$ converge uniformly where f maps from $[0, 3/4]$ to reals

Published on 18 Nov 2019 - 1:55

score 66 · Answer 5 · 2019-11-18 05:39:32

66

Views

Let $\Omega$ be a half-plane and $f_n$ a sequence of holomorphic functions on $\Omega$.

Published on 18 Nov 2019 - 5:39

score 54 · Answer 6 · 2019-11-18 05:56:29

54

Views

$\sum_{n=1}^{\infty} e^{-nx}x^n$ converges uniformly for $0 \leq x \leq 10$

Published on 18 Nov 2019 - 5:56

score 479 · Answer 7 · 2026-03-28 04:00:30

479

Views

Uniform Convergence Weierstrass' M-Test

Published on 28 Mar 2026 - 4:00

score 52 · Answer 8 · 2019-11-19 03:50:52

52

Views

Prove that for $f: [0, 1] \to \mathbb{R} , f_n(x) = \frac{nx}{1+n^2 x^2}$ is uniform convergent.

Published on 19 Nov 2019 - 3:50

score 28 · Answer 9 · 2026-03-29 03:36:37

28

Views

Prove $g(x) = \sum_{n=1}^{\infty} \frac{d}{dx}(-1)^n(4x)^n$ is uniformly continuous on $[-a,a]$ for each $a$ where $0 \lt a \lt \frac{1}{4}$.

Published on 29 Mar 2026 - 3:36

score 39 · Answer 10 · 2019-11-19 14:16:44

39

Views

Prove a uniform or non-uniform convergence of a functional sequence $f_n(x)=\arctan x^{3n} - \arctan x^{2n}$

Published on 19 Nov 2019 - 14:16

score 840 · Answer 11 · 2019-11-19 16:52:39

840

Views

Prove that the limit of a uniformly convergent sequence of bounded functions is bounded.

Published on 19 Nov 2019 - 16:52

score 424 · Answer 12 · 2026-03-27 07:18:40

424

Views

Is the space of smooth functions dense in that of continuous ones?

Published on 27 Mar 2026 - 7:18

score 29 · Answer 13 · 2019-11-19 22:05:00

29

Views

Showing Non-Uniform Convergence [Proof Verification]

Published on 19 Nov 2019 - 22:05

score 1.4k · Answer 14 · 2026-02-23 21:30:52

1.4k

Views

Counterexample around Dini's Theorem

Published on 23 Feb 2026 - 21:30

score 121 · Answer 15 · 2019-11-20 10:48:03

121

Views

Uniform convergence of difference quotient

Published on 20 Nov 2019 - 10:48

List Question

Maclaurin series of G(x)=$ \int_{0}^{x} \frac{1-e^{-y^2}}{y^2} \ dy $

Uniform/Pointwise Convergence

Proving the uniform convergence of $ f_n (x) = \sin(\frac{1}{n})\cos(x)$

Does $f_n(x) = \sum_{k=0}^n x^k$ converge uniformly where f maps from $[0, 3/4]$ to reals

Let $\Omega$ be a half-plane and $f_n$ a sequence of holomorphic functions on $\Omega$.

$\sum_{n=1}^{\infty} e^{-nx}x^n$ converges uniformly for $0 \leq x \leq 10$

Uniform Convergence Weierstrass' M-Test

Prove that for $f: [0, 1] \to \mathbb{R} , f_n(x) = \frac{nx}{1+n^2 x^2}$ is uniform convergent.

Prove $g(x) = \sum_{n=1}^{\infty} \frac{d}{dx}(-1)^n(4x)^n$ is uniformly continuous on $[-a,a]$ for each $a$ where $0 \lt a \lt \frac{1}{4}$.

Prove a uniform or non-uniform convergence of a functional sequence $f_n(x)=\arctan x^{3n} - \arctan x^{2n}$

Prove that the limit of a uniformly convergent sequence of bounded functions is bounded.

Is the space of smooth functions dense in that of continuous ones?

Showing Non-Uniform Convergence [Proof Verification]

Counterexample around Dini's Theorem

Uniform convergence of difference quotient

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