Decimal expansion of zeta(2) over the numbers that can be written as the sum of two squares, i.e. ., A001481.

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Equals 4/3/A243379/A334448.

Equals 4/3/A243379/A334448.Equals 4/3 * zeta_{2,0} (2) * zeta_{4,1} (2) * zeta_{4,3} (4), where zeta_{4,1} (2) = A175647. and zeta_{2,0} (s) = 2^s/(2^s - 1).

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Equals Product_{i > 0} 1/(1-A055025(i)^)^-2).

Cf. A000040, A001481, A055025, A175647, A243379, A334448.

allocatedDecimal expansion of zeta(2) over the numbers that can be written as the sum of fortwo A.Hsquares, i.Me. SmeetsA001481.

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

1,2

Close to the value of e^(3/2)/Pi.

R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT]], 2010-2015.

Equals Sum_{i > 0} 1/A001481(i)^2.

Equals Product_{i > 0} 1/(1-A055025(i)^2).

Equals 1/(1-prime(1)^(-2)) / Product_{i>1 and prime(i) == 1 (mod 4)} (1-prime(i)^(-2)) / Product_{i>1 and prime(i) == 3 (mod 4)} (1-prime(i)^(-4)), where prime(n) = A000040(n).

Equals 4/3/A243379/A334448.Equals 4/3 * zeta_{4,1} (2) * zeta_{4,3} (4), where zeta_{4,1} (2) = A175647.

1.4265560635125928786968093161550816361276693636770...

Cf. A001481, A055025, A175647, A243379, A334448.

Cf. A344124, A344125.

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nonn,cons

A.H.M. Smeets, May 09 2021

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