]]>https://www.mathisfunforum.com/profile.php?id=6822022-12-25T14:37:39Zhttps://www.mathisfunforum.com/viewtopic.php?pid=429792#p429792a double factorial products up 2 at a time not 1 2x!!=product k=1->x 2x so x+2n!!=x!!*product k=1->n 2x for something like a gamma function,we can take the log L(x)=ln(x!!) N is a huge number so ln(N+k)-ln(N)=0 for a little k compared to N L(N+2n)=L(N)+sum k=1->n ln(N+2k) =L(N)+sum k=1->n ln(N) =L(N)+nlnN now do some substitution L(2n)+sum k=1->N/2 ln(2n+2k)=sum k=1->N/2 ln(2k)+nlnN move it to right and merge sums L(2n)=sum k=1->N/2 -ln(2n+2k)+ ln(2k)+nlnN log rule L(2n)=sum k=1->N/2 ln(k/k+n)+nlnN sub n for 2n and exponentiate n!!=product k=1->N/2 k/k+n/2 +N^(n/2) minor changes n!!=product k=1->N/2 2k/k+n +sqrt(N^n) done! change the limits a bit N->2N^2 x->n x!!=lim N->inf 4*N^n*product k=1->N^2 k/(x+2k) idk if it actually works but i think it would cuz it based on the factorial video from lines that connect]]>https://www.mathisfunforum.com/profile.php?id=2417972022-12-25T12:04:23Zhttps://www.mathisfunforum.com/viewtopic.php?pid=429787#p429787