A255984 - OEIS

%I #20 Oct 01 2022 14:18:35

%S 2,1,7,0,8,0,3,7,6,3,6,7,4,8,0,2,9,7,8,0,8,9,0,4,3,8,8,1,8,7,2,3,8,7,

%T 3,0,3,6,1,6,3,2,6,6,8,4,3,5,3,6,3,7,7,8,0,9,2,8,6,3,6,9,8,3,3,1,1,1,

%U 0,4,6,1,5,8,5,8,8,8,7,1,8,5,7,5,0,3,4,8,8,4,4,7,0,4,3,4,6,5,4,1,2,8,9

%N Decimal expansion of sqrt(3*Pi/2), the value of an oscillatory integral.

%H G. C. Greubel, <a href="/A255984/b255984.txt">Table of n, a(n) for n = 1..10000</a>

%H David H. Bailey and Jonathan M. Borwein, <a href="http://www.davidhbailey.com/dhbpapers/oscillatory.pdf">Experimental computation with oscillatory integrals</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Limit_{p -> infinity} (integral_{0..infinity} abs(sin(t)/t)^p dt) = sqrt(3*Pi/2).

%e 2.17080376367480297808904388187238730361632668435363778...

%p evalf[120](sqrt(3*Pi/2)); # _Muniru A Asiru_, Mar 01 2019

%t RealDigits[Sqrt[3*Pi/2], 10, 103]//First

%o (PARI) sqrt(3*Pi/2) \\ _Charles R Greathouse IV_, Apr 20 2016

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(3*Pi(R)/2); // _G. C. Greubel_, Feb 28 2019

%o (Sage) numerical_approx(sqrt(3*pi/2), digits=100) # _G. C. Greubel_, Feb 28 2019

%Y Cf. A197723 (3*Pi/2).

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Mar 13 2015