0,8

Comment from R. W. Gosper (rwg(AT)sdf.lonestar.org), Jan 07 2009: (Start) Also numerator of (2/Pi)*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], {x, 0, Infinity}]: Using Mathematica 7.0, we have:

In[6]:= Table[2/Pi*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], {x, 0, Infinity}], {n, 8}]

Out[6]= {1, 1, 1, 1, 1, 1, 1, 467807924713440738696537864469/467807924720320453655260875000 }. The denominators of this sequence are given in A144616.

The last term is 1 - 491^7 / (2^3 3^12 5^6 7^7 11^6 13^6). (End)

Eric Weisstein's World of Mathematics, Borwein Integrals

i[n_] := Times@@(Sin[x/# ]&/@Range[1, n, 2])/x^((n+1)/2)/Pi; Numerator[Table[Integrate[i[n], {x, 0, \[Infinity]}], {n, 1, 19, 2}]]

Cf. A068215, A144616.

Sequence in context: A104300 A095450 A095452 this_sequence A144616 A095454 A058446

Adjacent sequences: A068211 A068212 A068213 this_sequence A068215 A068216 A068217

nonn,frac

Eric Weisstein (eric(AT)weisstein.com), Feb 21, 2002