A272873 - OEIS

%I #13 Oct 01 2022 15:35:56

%S 2,3,3,1,2,6,6,2,2,2,5,8,0,4,8,4,1,1,6,2,1,5,2,5,3,0,1,9,4,2,9,6,8,5,

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

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

%N Decimal expansion of the quadratic mean of 1 and Pi.

%C Quadratic mean (also known as the root mean square, rms) of two numbers x and y, is the Hoelder mean H(x,y,p) = ((x^2+y^2)/2)^(1/p) with p = 2.

%H Stanislav Sykora, <a href="/A272873/b272873.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Generalized_mean">Generalized mean</a>

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

%F Equals sqrt((1+Pi^2)/2).

%e 2.3312662225804841162152530194296857517396337769556644593068408873...

%t RealDigits[Sqrt[(1+Pi^2)/2],10,120][[1]] (* _Harvey P. Dale_, Apr 01 2018 *)

%o (PARI) sqrt((1+Pi^2)/2)

%Y Cf. A000796, A002388.

%Y Other means of 1 and Pi: A002161 (geometric, p=0), A191502 (AGM), A197733 (harmonic, p=-1), A269430 (arithmetic, p=1).

%K nonn,cons

%O 1,1

%A _Stanislav Sykora_, May 15 2016