A036791 Continued fraction for (2/Pi)*Integral_{x=0..Pi} sin(x)/x.

1, 5, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 6, 1, 1, 1, 1, 1, 9, 24, 1, 3, 1, 7, 1, 5, 1, 2, 2, 3, 1, 2, 2, 1, 8, 11, 4, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 23, 1, 3, 3, 1, 6, 2, 9, 1, 3, 2, 17, 1, 5, 3, 1, 8, 1, 1, 1, 1, 1, 4, 1, 5, 1, 2, 1, 38, 1, 5, 5, 2, 6, 2, 73, 1, 1, 1, 194, 27, 1, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

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

Examples

			1.178979744472167270232028845... = 1 + 1/(5 + 1/(1 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, Apr 28 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A036793 (decimal expansion).

Programs

Mathematica

ContinuedFraction[N[Integrate[Binomial[1, x], {x, 0, 1}], 120]] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 13 2006 *)

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

Extensions

Offset changed by Andrew Howroyd, Aug 03 2024