A122914 -id:A122914 - cp's OEIS frontend

A122915 Partial quotients of (1 + Log[2 Pi])/2, the entropy of the standard normal distribution.

1, 2, 2, 1, 1, 2, 2, 8, 1, 8, 4, 1, 4, 1, 3, 18, 1, 7, 1, 4, 2, 4, 2, 1, 2, 1, 4, 1, 1, 17, 1, 1, 1, 23, 1, 1, 2, 28, 3, 2, 4, 1, 2, 3, 1, 39, 12, 2, 1, 1, 120, 1, 6, 1, 5, 1, 1, 1, 1, 1, 1, 4, 3, 1, 1, 5, 1, 5, 14, 1, 3, 3, 1, 5, 1, 12, 2, 7, 2, 1

Offset: 0

Joseph Biberstine (jrbibers(AT)indiana.edu), Sep 18 2006

a = 1/2 - A075700; a = (1 + A061444)/2.

Decimal expansion in A122914.

ContinuedFraction[(1 + Log[2 Pi])/2, 80]

a = (1 + Log[2 Pi])/2

A386518 Decimal expansion of (log(2*Pi)-1)/2 + gamma.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Jul 24 2025

This is [x^2]G(x), the quadratic coefficient of the Taylor expansion of Barnes' G-function around zero. G(x) = x + this*x^2 -1.114914..*x^3 +O(x^4).

			0.9961541981062056023868418264880200709035568095777...

Paolo Xausa, Table of n, a(n) for n = 0..10000
R. J. Mathar, Erratum to Exercise A4.2 in "An introduction to the theory of the Riemann Zeta Function", viXra:2507.0094 (2025), coefficient h_2.
Wikipedia, Barnes G-function

Cf. A122914, A001620.

Maple
```
log(2*Pi)/2-1/2+gamma ; evalf(%) ;
```

First[RealDigits[(Log[2*Pi] - 1)/2 + EulerGamma, 10, 100]] (* Paolo Xausa, Jul 24 2025 *)

Equals A122914 -1 + A001620.

cp's OEIS Frontend

A122915 Partial quotients of (1 + Log[2 Pi])/2, the entropy of the standard normal distribution.

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