The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A176365

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A176365

Numerator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx.
(history; published version)

#20 by Bruno Berselli at Fri Dec 13 05:54:43 EST 2019

STATUS

reviewed

approved

#19 by Michel Marcus at Fri Dec 13 00:25:28 EST 2019

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proposed

reviewed

#18 by G. C. Greubel at Sun Dec 08 17:36:53 EST 2019

STATUS

editing

proposed

#17 by G. C. Greubel at Sun Dec 08 17:36:31 EST 2019

NAME

Numerator of (1/Pi)*Integral_{0..infinfinity} (sin x / x)^(2*n) dx.

EXAMPLE

a(2) = 1 because Integral[_{0..infinity] } (sin(x)/x)^4 dx = (1/3)*Pi.

a(3) = 11 because Integral[_{0..infinity] } (sin(x)/x)^6 dx = (11/40)*Pi.

a(4) = 151 because Integral[_{0..infinity] } (sin(x)/x)^8 dx = (151/630)*Pi.

a(5) = 15619 because Integral[_{0..infinity] } (sin^(10=2*5)(x)dx/x)^10 dx = (15619/72576)*Pi.

MATHEMATICA

a[n_] := (1/Pi )*Integrate[(Sin[x]/x)^(2n), {x, 0, Infinity}] // Numerator; Array[a, 16] (* _Jean-François Alcover_, Nov 25 2017 *)

Array[a, 16] (* Jean-François Alcover, Nov 25 2017 *)

STATUS

proposed

editing

#16 by Scott R. Shannon at Sun Dec 08 16:48:47 EST 2019

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editing

proposed

#15 by Scott R. Shannon at Sun Dec 08 16:46:58 EST 2019

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proposed

editing

#14 by G. C. Greubel at Sun Dec 08 15:53:42 EST 2019

STATUS

editing

proposed

Discussion

Sun Dec 08

16:46

Scott R. Shannon: Is 'sin^(10=2*5)(x)dx/x^10'  correct? Looks like a typo maybe.

#13 by G. C. Greubel at Sun Dec 08 15:53:17 EST 2019

LINKS

G. C. Greubel, <a href="/A176365/b176365.txt">Table of n, a(n) for n = 1..75</a>

STATUS

approved

editing

#12 by Alois P. Heinz at Sat Nov 25 18:47:46 EST 2017

STATUS

editing

approved

#11 by Alois P. Heinz at Sat Nov 25 18:36:37 EST 2017

STATUS

proposed

editing