Question

Estimate of remainder of Taylor expansion

score 32 · Answer 1 · 2026-04-09 14:25:07

32

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Estimate of remainder of Taylor expansion

Published on 09 Apr 2026 - 14:25

score 330 · Answer 2 · 2026-04-17 07:42:59

330

Views

Prove that $e^\frac{\pi}{2}=1+\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{5}{24}+\frac{1}{6}+\frac{85}{720}+\frac{520}{5040}+\frac{3145}{40320}+\cdots$

Published on 17 Apr 2026 - 7:42

score 152 · Answer 3 · 2026-04-16 03:09:37

152

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How can I represent the summation $\frac{x}{1^2}+\frac{x^2}{2^2}+\frac{x^3}{3^2}+\cdots$

Published on 16 Apr 2026 - 3:09

score 42 · Answer 4 · 2026-04-15 14:05:39

42

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Confluent Heun function $H(\gamma, \delta, \epsilon, \alpha, q, z) = 0$

Published on 15 Apr 2026 - 14:05

score 164 · Answer 5 · 2026-04-17 16:00:50

164

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Prove that $\dfrac{\pi^2}{16}=\dfrac{1}{2.2!}+\dfrac{3}{3.3!}+\dfrac{5}{3.4!}+\dfrac{8}{3.5!}+\cdots$

Published on 17 Apr 2026 - 16:00

score 24 · Answer 6 · 2026-04-10 16:13:35

24

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A problem about entire function and polynomial

Published on 10 Apr 2026 - 16:13

score 52 · Answer 7 · 2026-04-13 05:08:58

52

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Bounds on asymptotic behavior of Taylor coefficients of entire functions?

Published on 13 Apr 2026 - 5:08

score 86 · Answer 8 · 2026-04-09 10:23:02

86

Views

A conjecture involving series with zeta function

Published on 09 Apr 2026 - 10:23

score 23 · Answer 9 · 2026-04-11 13:03:34

23

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Spatial convolution of Taylor Expanded function which depends on isostable coordinates

Published on 11 Apr 2026 - 13:03

score 25 · Answer 10 · 2026-04-14 15:35:17

25

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Question about divergences of functions Vs divergences of their expansions

Published on 14 Apr 2026 - 15:35

score 87 · Answer 11 · 2026-04-17 04:50:38

87

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Taylor series expansion of $\frac{(1+x)}{1}+\frac{(1+x)^\frac{1}{3}}{3}+\frac{(1+x)^\frac{1}{5}}{5}+\cdots$

Published on 17 Apr 2026 - 4:50

score 36 · Answer 12 · 2026-04-25 22:29:07

36

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Find for which $a \in \mathbb{R}$ $\frac{e^x(1-\log x)}{x^3-x^2} = o(x^a)$ For $x \to 0^+$.

Published on 25 Apr 2026 - 22:29

score 124 · Answer 13 · 2026-04-14 13:28:05

124

Views

Taylor Series with (x-a) and delta x

Published on 14 Apr 2026 - 13:28

score 95 · Answer 14 · 2026-04-14 09:57:12

95

Views

Write the function $\log(1+x), x\in(-1,1]$ by expanding it into an infinite series by application of Taylor's Theorem.

Published on 14 Apr 2026 - 9:57

score 61 · Answer 15 · 2026-04-12 08:21:55

61

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Deriving a function with a given Taylor expansion

Published on 12 Apr 2026 - 8:21

List Question

Estimate of remainder of Taylor expansion

Prove that $e^\frac{\pi}{2}=1+\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{5}{24}+\frac{1}{6}+\frac{85}{720}+\frac{520}{5040}+\frac{3145}{40320}+\cdots$

How can I represent the summation $\frac{x}{1^2}+\frac{x^2}{2^2}+\frac{x^3}{3^2}+\cdots$

Confluent Heun function $H(\gamma, \delta, \epsilon, \alpha, q, z) = 0$

Prove that $\dfrac{\pi^2}{16}=\dfrac{1}{2.2!}+\dfrac{3}{3.3!}+\dfrac{5}{3.4!}+\dfrac{8}{3.5!}+\cdots$

A problem about entire function and polynomial

Bounds on asymptotic behavior of Taylor coefficients of entire functions?

A conjecture involving series with zeta function

Spatial convolution of Taylor Expanded function which depends on isostable coordinates

Question about divergences of functions Vs divergences of their expansions

Taylor series expansion of $\frac{(1+x)}{1}+\frac{(1+x)^\frac{1}{3}}{3}+\frac{(1+x)^\frac{1}{5}}{5}+\cdots$

Find for which $a \in \mathbb{R}$ $\frac{e^x(1-\log x)}{x^3-x^2} = o(x^a)$ For $x \to 0^+$.

Taylor Series with (x-a) and delta x

Write the function $\log(1+x), x\in(-1,1]$ by expanding it into an infinite series by application of Taylor's Theorem.

Deriving a function with a given Taylor expansion

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