Proposal: Keep tag gradshteyn-ryzhik for questions related to formulas found specifically in the book Table of Integrals, Series, and Products.
There are currently about 120 questions about formulas found in the above book, so I have tagged some of these questions with gradshteyn-ryzhik.
Altho...6
Recently, I made a lot of researches about equations about identities of combinatorics, suddenly I thought of a question:
What functions $f$ such that $\sum_{k=0}^n {n\choose k}^p f\left(k\right)$ has a closed form for some $p$ that $p$ is a real number $\ne0$?
There are lots of examples t...
2
Recently I asked a question about the sum of $\sum_{k=0}^n {n\choose k}^p f\left(k\right)$. Then, I was thinking of the case when $p=-1, f\left(x\right)=1$, which is $\sum_{k=0}^n \dfrac{1}{n\choose k}=\dfrac{1}{n\choose 0}+\dfrac{1}{n\choose 1}+\cdots+\dfrac{1}{n\choose n}$. I have substituted $...
2
Today I had a test about IMO which is pretty hard though, I have worked on a combinatoric question that I found a special formula:
$$\sum_{k=0}^n \left(k+1\right)\left(C^n_k\right)^2 = \dfrac{n+2}{2} C^{2n}_n$$
I don't know it is true or not, but it seems true because I have tested for some small...
With the short cut version of the $3x+1$ conjecture, $$f(x)=\frac {3x+1}{2},\text {if $x$ is odd }$$
and $$f(x)=\frac {x}{2},\text {if $x$ is even }$$
numerical experiments show that
$$ f^k(2^k-1)=3^{k}-1$$ is true for $k\ge 1$
$$ f^k(2^k-3)=3^{k-2}-1$$ is true for $k>3$
$$ f^k(2^k-11)=3^{k-4}...
