A333972 Decimal expansion of Pi^6/540 = zeta(2) * zeta(4).

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

Offset: 1

Author

Bernard Schott, Sep 29 2020

Keywords

• nonn
• cons

Comments

Compare 1st formula with Sum_{m>0, q>0} 1/(m^2*q^2) = Pi^4/36 = (zeta(2))^2 = A098198.

Examples

			1.78035035847278599450040637713411092382818060755749373322421516...
		

References

• Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.22, p. 275.

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A001157, A013661, A046951, A068447, A098198.

Programs

Maple

evalf(Pi^6/540,120);

Mathematica

RealDigits[Pi^6/540, 10, 100][[1]] (* Amiram Eldar, Sep 29 2020 *)

PARI

Pi^6/540 \\ Michel Marcus, Sep 30 2020

Formula

Equals Sum_{m>0, q>0, m | q} 1/(m^2*q^2).

Equals A013661 * A068447.

Equals Sum_{k>=1} sigma_2(k)/k^4. - Amiram Eldar, Sep 30 2020

Equals Sum_{k>=1} A046951(k)/k^2. - Amiram Eldar, Jan 25 2024