Question

For $p \in \mathbb{K}_{k}[X]$, the function $n \mapsto p(x_{0}+h n)$ is an arithmetic sequence of order $k$

score 89 · Answer 1 · 2026-03-26 04:34:06

89

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For $p \in \mathbb{K}_{k}[X]$, the function $n \mapsto p(x_{0}+h n)$ is an arithmetic sequence of order $k$

Published on 26 Mar 2026 - 4:34

score 2.8k · Answer 2 · 2026-04-06 06:37:14

2.8k

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How to derive derivative of the logarithm of a summation?

Published on 06 Apr 2026 - 6:37

score 83 · Answer 3 · 2026-03-25 22:03:26

83

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Singularity of a sum of Bessel functions

Published on 25 Mar 2026 - 22:03

score 101 · Answer 4 · 2026-03-27 23:31:03

101

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calculate a summation or a complex integral!

Published on 27 Mar 2026 - 23:31

score 328 · Answer 5 · 2026-04-04 07:36:43

328

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What do "$\Sigma$" and "$\Pi$" mean in trigonometry? (Eg, $\Pi \sin \left( A - \frac{\pi}{4} \right)$ and $\Sigma \tan A$)

Published on 04 Apr 2026 - 7:36

score 379 · Answer 6 · 2026-03-26 04:36:35

379

Views

Closed form for $\sum _{k=0}^n (-1)^k \binom{n}{k} \binom{n+k}{n} (H_n-H_k) x^k$

Published on 26 Mar 2026 - 4:36

score 40 · Answer 7 · 2019-07-20 21:19:34

How do you go from $\sum_{n \geq 3} \frac{1}{3} \big(\frac{1}{2}\big)^{n-2}s^n$ to $\frac{1}{6} s^3 \sum_{n \geq 0}\big(\frac{s}{2}\big)^{n}$?

score 273 · Answer 8 · 2019-07-20 22:49:32

273

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Sum of the first n terms of Central polygonal numbers (the Lazy Caterer's sequence)

Published on 20 Jul 2019 - 22:49

score 116 · Answer 9 · 2026-03-26 07:46:32

116

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How to manipulate $\frac{1}{\sin x}-\frac{1}{x}$ into $\sum_{k\geq 1}\left(\frac{1}{x-k\pi}+\frac{1}{x+k\pi}\right)(-1)^k$?

Published on 26 Mar 2026 - 7:46

score 77 · Answer 10 · 2019-07-21 14:08:23

77

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Finding the points of continuity of $f(x) =\sum_{n=1}^{\infty} \frac{\sin nx}{n^{1/2}}$

Published on 21 Jul 2019 - 14:08

score 240 · Answer 11 · 2026-03-28 02:23:45

240

Views

On an asymptotic improvement of AMM problem 11145 (April 2005)

Published on 28 Mar 2026 - 2:23

score 81 · Answer 12 · 2026-04-01 17:32:46

81

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For what $~K~$ does $~n~$ exist for all $~n\ge k~$ if $~n=6X+10Y+25Z~$ where $~n~$ and $~k~$ are natural numbers?

Published on 01 Apr 2026 - 17:32

score 94 · Answer 13 · 2026-04-04 05:19:39

94

Views

How to deal with modulo of $ \sum \binom{n}{r}$?

Published on 04 Apr 2026 - 5:19

score 901 · Answer 14 · 2026-04-01 18:04:32

901

Views

Solving equations of nested sums.

Published on 01 Apr 2026 - 18:04

score 87 · Answer 15 · 2026-03-27 01:42:28

87

Views

Simplifying sum involving combinations

Published on 27 Mar 2026 - 1:42

List Question

For $p \in \mathbb{K}_{k}[X]$, the function $n \mapsto p(x_{0}+h n)$ is an arithmetic sequence of order $k$

How to derive derivative of the logarithm of a summation?

Singularity of a sum of Bessel functions

calculate a summation or a complex integral!

What do "$\Sigma$" and "$\Pi$" mean in trigonometry? (Eg, $\Pi \sin \left( A - \frac{\pi}{4} \right)$ and $\Sigma \tan A$)

Closed form for $\sum _{k=0}^n (-1)^k \binom{n}{k} \binom{n+k}{n} (H_n-H_k) x^k$

How do you go from $\sum_{n \geq 3} \frac{1}{3} \big(\frac{1}{2}\big)^{n-2}s^n$ to $\frac{1}{6} s^3 \sum_{n \geq 0}\big(\frac{s}{2}\big)^{n}$?

Sum of the first n terms of Central polygonal numbers (the Lazy Caterer's sequence)

How to manipulate $\frac{1}{\sin x}-\frac{1}{x}$ into $\sum_{k\geq 1}\left(\frac{1}{x-k\pi}+\frac{1}{x+k\pi}\right)(-1)^k$?

Finding the points of continuity of $f(x) =\sum_{n=1}^{\infty} \frac{\sin nx}{n^{1/2}}$

On an asymptotic improvement of AMM problem 11145 (April 2005)

For what $~K~$ does $~n~$ exist for all $~n\ge k~$ if $~n=6X+10Y+25Z~$ where $~n~$ and $~k~$ are natural numbers?

How to deal with modulo of $ \sum \binom{n}{r}$?

Solving equations of nested sums.

Simplifying sum involving combinations

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