A242909 -id:A242909 - cp's OEIS frontend

A242910 Decimal expansion of exp(sqrt(Pi/24)).

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

Offset: 1

Jean-François Alcover, May 26 2014

			1.43591263161177312477224724028996545059...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 3.10 Kneser-Mahler polynomial constants p. 234.

G. C. Greubel, Table of n, a(n) for n = 1..5000
C. J. Smyth, On measures of polynomials in several variables, Bulletin of the Australian Mathematical Society, Volume 23 (1981), Issue 01.

Cf. A242908, A242909.

Digits:=100: evalf(exp(sqrt(Pi/24))); # Wesley Ivan Hurt, Jan 09 2017

RealDigits[Exp[Sqrt[Pi/24]], 10, 100] // First

exp(sqrt(Pi/24)) \\ G. C. Greubel, Jan 09 2017

Lim_(m->infinity) M(z_1 + (1 + z_2)*(1 + z_3)*...*(1 + z_m))^(1/sqrt(m)), where M is Mahler's measure for multivariate polynomials.

A242908 Decimal expansion of exp(7zeta(3)/(2Pi^2)).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, May 26 2014

			1.5315470966874577766407778651358020602...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 3.10 Kneser-Mahler polynomial constants, p. 234.

Antonio Gracia Llorente, Infinite Product Formula Involving the Apery's Constant, Zenodo Preprint, 2024.
C. J. Smyth, On measures of polynomials in several variables, Bulletin of the Australian Mathematical Society, Volume 23, Issue 1 (1981), pp. 49-63.

Cf. A002117, A242909, A242910.

RealDigits[Exp[7*Zeta[3]/(2*Pi^2)], 10, 100] // First

M(1 + x + y + z) where M is Mahler's measure for multivariate polynomials.

Equals sqrt(2) * Product_{k>=1} (1 + 1/(4*k^2 - 1))^(4*k^2) * (1 - 2/(2*k + 1))^k. - Antonio Graciá Llorente, Sep 02 2024

A244238 Decimal expansion of K = exp(8G/(3Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Jun 23 2014

			2.17601613529237042623516...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.10 Kneser-Mahler polynomial constants, p. 234.

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Bombieri Norm

Cf. A006752, A242908, A242909, A242910.

SetDefaultRealField(RealField(100)); R:=RealField(); Exp(8*Catalan(R)/(3*Pi(R))); // G. C. Greubel, Aug 25 2018

RealDigits[Exp[8*Catalan/(3*Pi)], 10, 102] // First

default(realprecision, 100); exp(8*Catalan/(3*Pi)) \\ G. C. Greubel, Aug 25 2018

cp's OEIS Frontend

A242910 Decimal expansion of exp(sqrt(Pi/24)).

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A242908 Decimal expansion of exp(7zeta(3)/(2Pi^2)).

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A244238 Decimal expansion of K = exp(8G/(3Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.

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cp's OEIS Frontend

A242910 Decimal expansion of exp(sqrt(Pi/24)).

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A242908 Decimal expansion of exp(7*zeta(3)/(2*Pi^2)).

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A244238 Decimal expansion of K = exp(8*G/(3*Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.

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Author

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Programs

Magma

Mathematica

PARI

A242908 Decimal expansion of exp(7zeta(3)/(2Pi^2)).

A244238 Decimal expansion of K = exp(8G/(3Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.