A377753 -id:A377753 - cp's OEIS frontend

A242822 Decimal expansion of B. Davis' constant Pi^2/(8*G), a Riesz-Kolmogorov constant, where G is Catalan's constant.

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

Offset: 1

Jean-François Alcover, May 23 2014

			1.3468852519994065951820075554411...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.7 Riesz-Kolmogorov Constants, p. 474.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001221, A002145, A004614, A006752, A111003, A330890, A377753.

SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/(8*Catalan(R)); // G. C. Greubel, Aug 25 2018

s:= convert(evalf(Pi^2/(8*Catalan), 140), string):
map(parse, subs("."=NULL, [seq(i, i=s)]))[]; # Alois P. Heinz, May 23 2014

RealDigits[Pi^2/(8*Catalan), 10, 100] // First

default(realprecision, 100); Pi^2/(8*Catalan) \\ G. C. Greubel, Aug 25 2018

(Sum_{n>=0} 1/(2*n + 1)^2) / (Sum_{n>=0} (-1)^n/(2*n + 1)^2) = A111003/A006752.
Equals Product_{k>=1} (1 + 1/A002145(k)^2)/(1 - 1/A002145(k)^2) = A243381 / A243379. - Vaclav Kotesovec, Apr 30 2020
Equals Sum_{q in A004614} 2^A001221(q)/q^2. - R. J. Mathar, Jan 27 2021
Equals 1/A377753. - Hugo Pfoertner, Nov 22 2024

A383851 Decimal expansion of exp(8G/Pi)((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, May 13 2025

			4.4312013071941991970823677283552872932838015281012...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Michael Penn, A beautiful Ramanujan product, YouTube video, 2025.

Cf. A006752, A049006, A377753.

First[RealDigits[Exp[8*Catalan/Pi]*((1 - #)/(1 + #))^2 & [Exp[-Pi/2]], 10, 100]]

Equals Product_{i=0..oo} (1 + 4/(2*i+1)^4)^((-1)^i*(2*i+1)) (from Ramanujan).

cp's OEIS Frontend

A242822 Decimal expansion of B. Davis' constant Pi^2/(8*G), a Riesz-Kolmogorov constant, where G is Catalan's constant.

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A383851 Decimal expansion of exp(8G/Pi)((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).

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cp's OEIS Frontend

A242822 Decimal expansion of B. Davis' constant Pi^2/(8*G), a Riesz-Kolmogorov constant, where G is Catalan's constant.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A383851 Decimal expansion of exp(8*G/Pi)*((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).

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Author

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Examples

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Programs

Mathematica

Formula

A383851 Decimal expansion of exp(8G/Pi)((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752).