Question

Why is $\int_{0}^{\infty} f(t)x^tdt$ the continuous version of the power series $\sum_{0}^{\infty} f(n)x^n$?

score 33 · Answer 1 · 2019-09-23 02:52:24

33

Views

Why is $\int_{0}^{\infty} f(t)x^tdt$ the continuous version of the power series $\sum_{0}^{\infty} f(n)x^n$?

Published on 23 Sep 2019 - 2:52

score 125 · Answer 2 · 2026-03-27 21:36:21

125

Views

Are functions of the form $f(x)=A\sin(x)+B\cos(x)$ the only ones satisfying $f'(x)=f(x+\pi/2)$?

Published on 27 Mar 2026 - 21:36

score 134 · Answer 3 · 2019-09-23 12:34:21

134

Views

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score 1.2k · Answer 4 · 2026-04-03 05:46:57

1.2k

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score 152 · Answer 5 · 2026-03-25 06:04:01

152

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score 98 · Answer 6 · 2026-03-25 07:44:42

98

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score 124 · Answer 7 · 2019-09-25 06:28:53

124

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score 108 · Answer 8 · 2026-04-02 16:38:06

108

Views

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score 47 · Answer 9 · 2026-03-25 11:16:50

47

Views

$f(x)= \frac{1}{x^{2}-3x-4} $The power series expansion at x = 1.

Published on 25 Mar 2026 - 11:16

score 100 · Answer 10 · 2019-10-01 05:42:42

100

Views

How to prove $\lim_{x\to 0}\sum^\infty_{k=0}\frac{(-1)^k}{k!}x^{-2k}=0$?

Published on 01 Oct 2019 - 5:42

score 275 · Answer 11 · 2026-03-27 00:01:07

275

Views

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Published on 27 Mar 2026 - 0:01

score 22 · Answer 12 · 2019-10-02 02:09:22

22

Views

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Published on 02 Oct 2019 - 2:09

score 323 · Answer 13 · 2026-04-02 14:08:08

323

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score 103 · Answer 14 · 2014-03-12 10:09:29

103

Views

How do I simplify the formal power series $1+2x^2F(x)^2$?

Published on 12 Mar 2014 - 10:09

score 594 · Answer 15 · 2014-03-12 17:23:35

594

Views

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Published on 12 Mar 2014 - 17:23

List Question

Why is $\int_{0}^{\infty} f(t)x^tdt$ the continuous version of the power series $\sum_{0}^{\infty} f(n)x^n$?

Are functions of the form $f(x)=A\sin(x)+B\cos(x)$ the only ones satisfying $f'(x)=f(x+\pi/2)$?

Norm of Ratio of Operators

Nonanalytic functions with Taylor Series

Transforming a Power series to a Chebyshev expansion

Can the b-ary power series of an irrational number evaluate to a rational number?

Converting power series to an equation

Show recursive formula for coefficients in power series, and use them to evaluate a contour integral

$f(x)= \frac{1}{x^{2}-3x-4} $The power series expansion at x = 1.

How to prove $\lim_{x\to 0}\sum^\infty_{k=0}\frac{(-1)^k}{k!}x^{-2k}=0$?

Power Series Coefficients and Poles

arbitrary order differentiation of a product of functions

Power series centered at $x =0$

How do I simplify the formal power series $1+2x^2F(x)^2$?

Find the radius of convergence of the power series

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