Question

Proof that the product of two Maclaurin series forms a valid Maclaurin Series

score 80 · Answer 1 · 2026-04-17 01:17:35

80

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Proof that the product of two Maclaurin series forms a valid Maclaurin Series

Published on 17 Apr 2026 - 1:17

score 260 · Answer 2 · 2026-03-26 12:36:45

260

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Conditions to calculate an integral through a series expansion

Published on 26 Mar 2026 - 12:36

score 133 · Answer 3 · 2026-04-11 09:29:23

133

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Is it possible to express any antiderivative as an infinite sum using integration by parts?

Published on 11 Apr 2026 - 9:29

score 61 · Answer 4 · 2026-04-17 14:41:05

61

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Proving $Y(x_{n+1}) = Y(x_n) + \frac{h}{2}\bigl[Y'(x_n) + Y'(x_{n+1}) \bigr]\\ - \frac{h^3}{24} \bigl[Y^{(3)}(x_n)+Y^{(3)}(x_{n+1})\bigr]+O(h^5)$

Published on 17 Apr 2026 - 14:41

score 41 · Answer 5 · 2026-04-14 09:40:05

41

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what is the formular of k-total derivative of vector-valued function

Published on 14 Apr 2026 - 9:40

score 52 · Answer 6 · 2026-04-14 12:16:20

52

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Can $\sum _{k=0}^n \frac {\sin(\frac {k\pi}2)}{k!}x^k$ be the $n$th Maclaurin polynomial of $\sin x$?

Published on 14 Apr 2026 - 12:16

score 56 · Answer 7 · 2026-04-17 12:43:30

56

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Why does $-\left(\frac{1}{2}\right) \frac{d^2}{d x^2} \frac{1}{1-x}=-\sum_{n=0}^{\infty}\left(\frac{(n+2)(n+1) x^n}{2}\right)$?

Published on 17 Apr 2026 - 12:43

score 113 · Answer 8 · 2026-04-24 03:55:04

113

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Confused about terminology for the center of power series; what does "centered at $x=1$" mean?

Published on 24 Apr 2026 - 3:55

score 40 · Answer 9 · 2026-04-10 06:15:36

40

Views

Application of multidimensional Taylor's Formula

Published on 10 Apr 2026 - 6:15

score 114 · Answer 10 · 2026-04-10 13:34:45

114

Views

How to calculate the weights for Discrete Laplacian Operator?

Published on 10 Apr 2026 - 13:34

score 261 · Answer 11 · 2026-04-15 20:15:19

261

Views

Taylor expansion of $\frac{\operatorname{arctanh}(x)}{1+x^2}$

Published on 15 Apr 2026 - 20:15

score 56 · Answer 12 · 2026-04-17 06:57:31

56

Views

Is there an analytic $f(x)$ such that $\int_{a}^{b} f(x) \neq \sum_{k=0}^\infty{\int_a^b{T_k(x)}}$

Published on 17 Apr 2026 - 6:57

score 80 · Answer 13 · 2026-03-26 16:05:21

80

Views

What determines the coefficients of the laplacian filter?

Published on 26 Mar 2026 - 16:05

score 42 · Answer 14 · 2026-04-13 02:39:34

42

Views

Laurent Expansion at specific singularity

Published on 13 Apr 2026 - 2:39

score 59 · Answer 15 · 2026-04-10 18:25:07

59

Views

Asymptotic formula for cot(x).

Published on 10 Apr 2026 - 18:25

List Question

Proof that the product of two Maclaurin series forms a valid Maclaurin Series

Conditions to calculate an integral through a series expansion

Is it possible to express any antiderivative as an infinite sum using integration by parts?

Proving $Y(x_{n+1}) = Y(x_n) + \frac{h}{2}\bigl[Y'(x_n) + Y'(x_{n+1}) \bigr]\\ - \frac{h^3}{24} \bigl[Y^{(3)}(x_n)+Y^{(3)}(x_{n+1})\bigr]+O(h^5)$

what is the formular of k-total derivative of vector-valued function

Can $\sum _{k=0}^n \frac {\sin(\frac {k\pi}2)}{k!}x^k$ be the $n$th Maclaurin polynomial of $\sin x$?

Why does $-\left(\frac{1}{2}\right) \frac{d^2}{d x^2} \frac{1}{1-x}=-\sum_{n=0}^{\infty}\left(\frac{(n+2)(n+1) x^n}{2}\right)$?

Confused about terminology for the center of power series; what does "centered at $x=1$" mean?

Application of multidimensional Taylor's Formula

How to calculate the weights for Discrete Laplacian Operator?

Taylor expansion of $\frac{\operatorname{arctanh}(x)}{1+x^2}$

Is there an analytic $f(x)$ such that $\int_{a}^{b} f(x) \neq \sum_{k=0}^\infty{\int_a^b{T_k(x)}}$

What determines the coefficients of the laplacian filter?

Laurent Expansion at specific singularity

Asymptotic formula for cot(x).

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