A036790 Continued fraction for Integral_{x=0..Pi} sin(x)/x.

1, 1, 5, 1, 3, 15, 1, 5, 3, 2, 7, 2, 1, 62, 1, 3, 110, 1, 39, 1, 1, 1, 4, 3, 1, 2, 5, 2, 2, 28, 1, 1, 1, 2, 6, 2, 2, 1, 278, 3, 3, 1, 1, 4, 1, 4, 2, 5, 5, 2, 4, 1, 1, 1, 28, 1, 1, 203, 1, 89, 2, 2, 2, 1, 12, 1, 1, 3, 33, 1, 8, 3, 1, 2, 6, 1, 1, 3, 256, 1, 6, 5, 1, 6, 14, 1

Offset

1,3

Comments

Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... - Harry J. Smith, May 01 2009

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

1.851937051982466170361053370... = 1 + 1/(1 + 1/(5 + 1/(1 + 1/(3 + ...)))). - Harry J. Smith, May 01 2009

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=contfrac(x); for (n=1, 20000, write("b036790.txt", n, " ", x[n])); } \\ Harry J. Smith, May 01 2009

Crossrefs

Cf. A036792.

Sequence in context: A365456 A134894 A143700 * A201847 A185559 A275842

Adjacent sequences: A036787 A036788 A036789 * A036791 A036792 A036793

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved