Eulerin vakio

Eulerin vakio ℮ ja sen laskeminen


Tai kuka tietää, onko tämäkään vakio?
= 2.71828182845904523536028747135266249775724709369995...

Among many other things, ℮ is also the limit of  (1 + 1/n ) as n tends to infinity.

e-limit

 e=lim_(x->infty)(1+1/x)^x   1)


The letter e may now no longer be used to denote anything other than this positive universal constant.
Edmund Landau (1877-1938).

Gentlemen, we have not the slightest idea what this equation means,
but we may be sure that it means something very important

Benjamin Peirce (1809-1880).

No, samaan tulokseen tulin minäkin vuosina 1976-1981. Mikkeilin Tekussa.

This is a tiny C program from Xavier Gourdon (Jul 1999)
to compute 9000 decimal digits of ℮ on your computer.
		  main(){
			  int N=9009,n=N,a[9009],x;
			  while(--n)
				  a[n]=1+1/n;
			  for(;N>9; printf("%d",x))
				  for(n=N--;--n;a[n]=x%n,x=10*a[n-1]+x/n);
		  }
		  
1) Wolfram Mathworld
Kääntyyy samalla cc komenolla kuin Linuxissa yleensäkin.