OFFSET
0,1
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
FORMULA
Equals sqrt(A019683). - Michel Marcus, Aug 31 2014
From A.H.M. Smeets, Sep 22 2018: (Start)
Equals Integral_{x >= 0} sin(8x)/sqrt(x) dx [Gradshteyn and Ryzhik].
Equals Integral_{x >= 0} cos(8x)/sqrt(x) dx [Gradshteyn and Ryzhik]. (End)
From Amiram Eldar, Aug 13 2020: (Start)
Equals Integral_{x=0..oo} x * exp(-x^4) dx.
Equals Integral_{x=0..oo} x^2 * exp(-x^2) dx. (End)
EXAMPLE
0.44311346272637900682454187083528629569938736403059678...
MAPLE
evalf(sqrt(Pi)/4, 120); # Muniru A Asiru, Sep 22 2018
MATHEMATICA
First[RealDigits[Sqrt[Pi]/4, 10, 100]] (* Paolo Xausa, May 02 2024 *)
PROG
(PARI) sqrt(Pi)/4 \\ Altug Alkan, Sep 22 2018
(PARI) intnum(x=0, [oo, -8*I], sin(8*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
(PARI) intnum(x=[0, -1/2], [oo, 8*I], cos(8*x)/sqrt(x)) \\ Gheorghe Coserea, Sep 23 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved