A087198 -id:A087198 - cp's OEIS frontend

A087197 Decimal expansion of 1/sqrt(Pi).

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

Offset: 0

Sven Simon, Aug 24 2003

Radius of a circle with area 1.

Expectation of the maximum of a size 2 sample from a normal (0,1) distribution. - Jean-François Alcover, Jun 05 2014

			0.56418958354775628694...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365.

G. C. Greubel, Table of n, a(n) for n = 0..5000
Eric Weisstein's World of Mathematics, Inverse Erf
Index entries for transcendental numbers

Cf. A086201, A087198, A087199.

RealDigits[1/Sqrt[Pi], 10, 50][[1]] (* G. C. Greubel, Jan 09 2017 *)

Pi^-.5 \\ Charles R Greathouse IV, Nov 13 2015

Equals lim_{n -> infinity} Catalan(n)/(4^n*n^(-3/2)). - Jean-François Alcover, May 23 2013

Equals Sum_{k>=1} k/(2^k * Gamma(k+3/2)). - Amiram Eldar, May 27 2021

A232808 Decimal expansion of the surface area of a 3D sphere with unit volume.

Original entry on oeis.org

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

Offset: 1

Stanislav Sykora, Nov 30 2013

More generally, the ratio (surface)/(volume)^(2/3), characteristic of the shape of a bounded 3D body, which is invariant under linear scaling and known as the surface index. Its common value for all spheres is the smallest possible among all closed 3D bodies (for a cube, for example, it is exactly 6.0).

			4.83597586204940892215090053991785481683384221697158466707687622613685...

Stanislav Sykora, Table of n, a(n) for n = 1..2000
Index entries for transcendental numbers

Cf. A000796 (Pi), A019673 (Pi/6); other sphere metrics: A019694, A019699, A087198, A087199.

RealDigits[(36 Pi)^(1/3), 10, 90][[1]] (* Bruno Berselli, Dec 01 2013 *)

(36*Pi)^(1/3) = 6*A019673^(1/3).

A019707 Decimal expansion of sqrt(Pi)/5.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

With offset 1 this is the decimal expansion of 2*sqrt(Pi) = 3.544907..., which is the smallest possible perimeter index eta=P/sqrt(A) of all figures (not necessarily connected) in the Euclidean plane with a continuous boundary of length P (perimeter) enclosing a finite area A. The smallest value is attained only by a Euclidean planar disk. For example, eta=4 for squares, eta=2(sqrt(a/b)+sqrt(b/a))>=4 for aXb rectangles, and eta=4.559014... (A268604) for equilateral triangles. - Stanislav Sykora, Feb 08 2016

			0.3544907701811...= 0.2*A002161.

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for transcendental numbers

Cf. A000796, A002161, A087198, A268604.

RealDigits[Sqrt[Pi]/5, 10, 100][[1]] (* Alonso del Arte, Jun 10 2012 *)

sqrt(Pi)/5 \\ Charles R Greathouse IV, Sep 28 2022

sqrt(Pi)/5 = sqrt(4 * Pi)/10.

Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. - Lee A. Newberg, Mar 05 2024

A087199 Decimal expansion of (3/(4*Pi))^(1/3).

Original entry on oeis.org

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

Offset: 0

Sven Simon, Aug 24 2003

Radius of a sphere of volume 1.

			0.62035049089940001666800681204777816735078620018600162009895688991314690606003....

Index entries for transcendental numbers

Cf. A086201, A087197, A087198.

RealDigits[(3/(4 Pi))^(1/3), 10, 111][[1]] (* Robert G. Wilson v, Sep 29 2014 *)

A073001 Decimal expansion of Bernstein's constant.

Original entry on oeis.org

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

Offset: 0

Robert G. Wilson v, Aug 03 2002

Named after the Russian and Soviet mathematician Sergei Natanovich Bernstein (1880-1968). - Amiram Eldar, Jun 06 2021

			0.2801694990238691330364364912306720000424821398...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 4.4, p. 258.

Serge Bernstein, Sur la meilleure approximation de |x| par des polynomes de degrés donnés, [in French], Acta Math., Vol. 37 (1913), pp. 1-57.
Simon Plouffe, The Bernstein Constant. [broken link]
R. S. Varga and A. J. Carpenter, A conjecture of S. Bernstein in approximation theory. [in Russian], Mat. Sb. (N.S.), 1986, Volume 129(171), Number 4, Pages 535-548, English version, Mathematics of the USSR-Sbornik, Volume 57, Number 2.
Richard S. Varga and Amos J. Carpenter, On the Bernstein Conjecture in Approximation Theory, Constr. Approx. 1(1), 333-348, December 1985
Eric Weisstein's World of Mathematics, Bernstein's Constant.
Wikipedia, Bernstein's constant.

Cf. A087198 (the value conjectured by Bernstein in 1913).

A378942 Decimal expansion of (1/sqrt(Pi) + e*erfc(-1))/2.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Dec 11 2024

			2.7865848321550198766289520248877912002691926567823...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 4.6, p. 262.

Cf. A001113, A019739, A087197, A087198, A099286, A222392.

RealDigits[(1/Sqrt[Pi]+E Erfc[-1])/2,10,100][[1]]

Equals (1 + e*sqrt(Pi)*(1 + erf(1)))/(2*sqrt(Pi)).

Equals A222392 / 2. - Amiram Eldar, Feb 15 2025

cp's OEIS Frontend

A087197 Decimal expansion of 1/sqrt(Pi).

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A232808 Decimal expansion of the surface area of a 3D sphere with unit volume.

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A019707 Decimal expansion of sqrt(Pi)/5.

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A087199 Decimal expansion of (3/(4*Pi))^(1/3).

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A073001 Decimal expansion of Bernstein's constant.

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A378942 Decimal expansion of (1/sqrt(Pi) + e*erfc(-1))/2.

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