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1h
reviewed Approve counting steps in Collatz Sequence
2h
comment Boolean Algebra - Simplify $A(C+D'B)+A'$
Hint: $X+YZ=(X+Y)(X+Z).$
3h
revised On a “coincidence” of two sequences involving $a_n = {_2F_1}\left(\tfrac{1}{2},-n;\tfrac{3}{2};\tfrac{1}{2}\right)$
Replaced 1/2 with -1/2.
1d
comment Finding the integral of a 1/variable*radical function
@Andrew: Applying the same trick again $($i.e., multiplying both numerator and denominator by $u),$ and letting $w=u^2-9,$ then substituting $w=t^2,$ I get $\displaystyle\int\frac{dt}{t^2+9}=\frac13~\arctan\frac t3$
1d
comment A closed form for the following Series
Even the simpler series $\displaystyle\sum_{k=1}^\infty\frac{k!}{k^k}$ is not known to possess a closed form. See OEIS A$94082$.
1d
comment Integral of combination of power, exponential, and kummer hypergeometric function
For $b=0$ we have this result. Otherwise, I'm at a loss.
1d
comment Last digit of $235!^{69}$
Also, its first digit is $1,$ and its middle digit is $4.$
2d
answered Root of the $\zeta(s) = s$
2d
comment Is there a nice closed form to $\int_0^{\pi/2} (\log \sin x)^n\text{ d}x$ for $n\in \Bbb{Q},n\gt 1$?
Welcome back ! :-$)$
2d
comment Is it possible to find a perfect cube like 111…11?
No solutions below $10^4$ digits.
2d
comment Riemann zeta function at $\Re(s)=0$ and $\Re(s)=1$
See also the functional equation and the particular values at negative integers of the Riemann $\zeta$ function.
2d
comment Riemann zeta function at $\Re(s)=0$ and $\Re(s)=1$
We also have $~\lim\limits_{x\to0^\pm}\zeta(1+x)-\dfrac1x=\gamma,~$ see Euler-Mascheroni constant for more information.
2d
answered Riemann zeta function at $\Re(s)=0$ and $\Re(s)=1$
2d
comment How can I prove that only there continuous odd prime are $3,5,7$?
Hint: All primes except for $2$ and $3$ are of the form $6n\pm1.$
2d
comment How many answers to $|3^x-2^y|=5$?
See Pillai's conjecture.
2d
comment Books or website about solving IMO problems
See IMO Math.
2d
comment Divisibility: $60 \mid (2x-y)(2y-z)(3z+2x)$, if $8x-10y+27z=0$
$27z=2~(5y-4x)~=>~z=2t~=>~15\mid(2x-y)(y-t)(x+3t).$
2d
comment The closed form of $\int^\infty_{B}e^{-(x+\frac{A}{x})}\,dx$, where $A>0$, $B>0$.
This question is equivalent to whether there are any incomplete Bessel functions.
2d
comment Prove equivalence between two Bessel functions relations
A related question.
2d
comment Estimate from above the series: $\sum_{i=1}^n \frac{1}{(i-j)^2}$.
Hint: $~\displaystyle{\sum_{i=1}^n}_{(i\neq j)}=\sum_{i=1}^{j-1}+\sum_{i=j+1}^n~$