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

%I A333972 #45 Jan 25 2024 02:46:33
%S A333972 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,
%T A333972 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,
%U A333972 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
%N A333972 Decimal expansion of Pi^6/540 = zeta(2) * zeta(4).
%C A333972 Compare 1st formula with Sum_{m>0, q>0} 1/(m^2*q^2) = Pi^4/36 = (zeta(2))^2 = A098198.
%D A333972 Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.22, p. 275.
%H A333972 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A333972 Equals Sum_{m>0, q>0, m | q} 1/(m^2*q^2).
%F A333972 Equals A013661 * A068447.
%F A333972 Equals Sum_{k>=1} sigma_2(k)/k^4. - _Amiram Eldar_, Sep 30 2020
%F A333972 Equals Sum_{k>=1} A046951(k)/k^2. - _Amiram Eldar_, Jan 25 2024
%e A333972 1.78035035847278599450040637713411092382818060755749373322421516...
%p A333972 evalf(Pi^6/540,120);
%t A333972 RealDigits[Pi^6/540, 10, 100][[1]] (* _Amiram Eldar_, Sep 29 2020 *)
%o A333972 (PARI) Pi^6/540 \\ _Michel Marcus_, Sep 30 2020
%Y A333972 Cf. A001157, A013661, A046951, A068447, A098198.
%K A333972 nonn,cons
%O A333972 1,2
%A A333972 _Bernard Schott_, Sep 29 2020