A068214 Numerator of Borwein integral of order 2n+1.

1, 1, 1, 1, 1, 1, 1, 467807924713440738696537864469, 17708695183056190642497315530628422295569865119, 8096799621940897567828686854312535486311061114550605367511653, 2051563935160591194337436768610392837217226815379395891838337765936509

Offset

0,8

Comments

From Bill Gosper, Jan 07 2009: (Start)

The 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)

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..12

J. M. Borwein, The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems, 2014; Chapter prepared for John Monaghan, Luc Troche and Jonathan Borwein, "Tools and mathematics: Instruments for learning", Spring-Verlag, 2015.

Eric Weisstein's World of Mathematics, Borwein Integrals

Wikipedia, Borwein integral (From N. J. A. Sloane, Feb 25 2012)

Mathematica

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}]]

Crossrefs

Cf. A068215, A144616.

Sequence in context: A217407 A280350 A095452 * A144616 A095454 A261700

Adjacent sequences: A068211 A068212 A068213 * A068215 A068216 A068217

Keyword

nonn,frac,changed

Author

Eric W. Weisstein, Feb 21 2002

Status

approved