A269430 -id:A269430 - cp's OEIS frontend

A272873 Decimal expansion of the quadratic mean of 1 and Pi.

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, 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, 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

Offset: 1

Stanislav Sykora, May 15 2016

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.

			2.3312662225804841162152530194296857517396337769556644593068408873...

Stanislav Sykora, Table of n, a(n) for n = 1..1000
Wikipedia, Generalized mean
Index entries for transcendental numbers

Cf. A000796, A002388.

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

RealDigits[Sqrt[(1+Pi^2)/2],10,120][[1]] (* Harvey P. Dale, Apr 01 2018 *)

PARI
```
sqrt((1+Pi^2)/2)
```

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

cp's OEIS Frontend

A272873 Decimal expansion of the quadratic mean of 1 and Pi.

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