OFFSET
0,2
COMMENTS
Continued fraction expansion for Integrate[Binomial[1,x], {x,0,1}]. - Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 13 2006
Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... - Harry J. Smith, Apr 28 2009
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..19999
G. Xiao, Contfrac
EXAMPLE
1.178979744472167270232028845... = 1 + 1/(5 + 1/(1 + 1/(1 + 1/(2 + ...)))). - Harry J. Smith, Apr 28 2009
MATHEMATICA
ContinuedFraction[N[Integrate[Binomial[1, x], {x, 0, 1}], 120]] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 13 2006 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 21000); y=0; x=Pi; m=x; x2=x*x; n=1; nf=1; s=1; while (x!=y, y=x; n++; nf*=n; n++; nf*=n; m*=x2; s=-s; x+=s*m/(n*nf)); x*=2/Pi; x=contfrac(x); for (n=1, 20000, write("b036791.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 28 2009
CROSSREFS
KEYWORD
nonn,cofr
AUTHOR
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 03 2024
STATUS
approved