A085508 Decimal expansion of conjectured value for the Bloch constant.

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

Offset

0,1

Comments

Named after the French mathematician André Bloch (1893-1948). - Amiram Eldar, Jun 17 2021

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 7.1, pp. 456-459.

Links

Table of n, a(n) for n=0..101.

L. V. Alfors and H. Grunsky, Über die Blochsche Konstante, Mathematische Zeitschrift, Vol. 30, No. 1 (1929), pp. 608-634.

Michèle Audin, Mathématiques en asile d’aliénés, Images des Mathématiques, CNRS, 2014.

André Bloch, Les théorèmes de M. Valiron sur les fonctions entières et la théorie de l'uniformisation, Annales de la faculté des sciences de Toulouse, Sér. 3, Vol. 17 (1925), pp. 1-22.

Eric Weisstein's World of Mathematics, Bloch Constant.

Formula

Equals 2^(3/4) * Pi^(3/2) / (3^(3/8) * Gamma(1/4)^2). - Vaclav Kotesovec, Jan 09 2026

Equals Pi / (A062539 * 12^(3/8)) [Guido Vranken]. - Vaclav Kotesovec, Feb 13 2026

Example

0.47186165345268178487446879361131614907701262173944...

Mathematica

RealDigits[Gamma[1/3]*Gamma[11/12]/(Sqrt[1 + Sqrt[3]]*Gamma[1/4]), 10, 100][[1]]
RealDigits[2^(3/4) * Pi^(3/2) / (3^(3/8) * Gamma[1/4]^2), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Crossrefs

Cf. A062539.

Sequence in context: A393484 A021216 A335006 * A198347 A388552 A388436

Adjacent sequences: A085505 A085506 A085507 * A085509 A085510 A085511

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 02 2003

Status

approved