A123092 - OEIS

A123092

Decimal expansion of Sum_{k>=1} 1/((2k-1)^2(2k+1)^2) = (Pi^2-8)/16.

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

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OFFSET

0,3

REFERENCES

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See exercise 109 at page 269.

Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley and Sons, Inc., NJ, 2006, page 506.

LINKS

Table of n, a(n) for n=0..104.

Index entries for transcendental numbers.

FORMULA

Equals (A111003-1)/2. - Hugo Pfoertner, Aug 20 2024

Equals Sum_{k>=1} 1/(4*k^2-1)^2. - Sean A. Irvine, Mar 29 2025