A396374 Decimal expansion of the determinant of the Laplacian on S^7, the 7-dimensional unit sphere, with the standard metric induced by the R^8 Euclidean norm.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

José Cunha and Pedro Freitas, Recurrence formulae for spectral determinants, Journal of Number Theory, Vol. 267 (2025), pp. 134-175; arXiv preprint, arXiv:2404.12114 [math.SP], 2024. See Corollary 2.9, p. 16.

Formula

Equals (Pi/3) * exp(949*zeta(3)/(720*Pi^2) - 13*zeta(5)/(24*Pi^4) + zeta(7)/(32*Pi^6)).

Example

1.222521243741051798580285546613412059282832656608533...

Mathematica

RealDigits[(Pi/3) * Exp[949*Zeta[3]/(720*Pi^2) - 13*Zeta[5]/(24*Pi^4) + Zeta[7]/(32*Pi^6)], 10, 120][[1]]

Prog

(PARI) (Pi/3) * exp(949*zeta(3)/(720*Pi^2) - 13*zeta(5)/(24*Pi^4) + zeta(7)/(32*Pi^6))

Crossrefs

Determinant of the Laplacian on S^n: A212002 (n=1), A396369 (n=2), A396370 (n=3), A396371 (n=4), A396372 (n=5), A396373 (n=6), this constant (n=7), A396375 (n=8), A396376 (n=9).

Cf. A002117, A013663, A013665.

Sequence in context: A285441 A088885 A232736 * A275887 A121358 A271321

Adjacent sequences: A396371 A396372 A396373 * A396375 A396376 A396377

Keyword

nonn,cons

Author

Amiram Eldar, May 24 2026

Status

approved