A152649 Decimal expansion of Pi^4/72.
1, 3, 5, 2, 9, 0, 4, 0, 4, 2, 1, 3, 8, 9, 2, 2, 7, 3, 9, 3, 9, 5, 0, 0, 4, 6, 2, 0, 6, 7, 6, 4, 5, 9, 8, 7, 8, 4, 6, 8, 4, 3, 8, 6, 8, 9, 8, 9, 8, 4, 0, 8, 6, 3, 4, 6, 0, 3, 7, 2, 0, 2, 6, 9, 3, 0, 5, 1, 5, 0, 7, 7, 0, 2, 3, 3, 7, 1, 1, 0, 5, 8, 1, 9, 6, 1, 3, 7, 0, 4, 4, 9, 2, 7, 1, 2, 4, 8, 9, 6, 5, 4, 1, 2, 3
Offset: 1
Examples
Equals 1.352904042138922739395004620676459878468438689898408634603...
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..2000
- David Borwein and J. M. Borwein, On an intriguing integral and some series related to zeta(4), Proc. Am. Math. Soc. 123 (1995), 1191-1198.
- I. Gradsteyn and I. Ryzhik, Table of integrals, series and products, Academic Press, 1980, page 7 (formulas from 0.233.3 to 0.233.5).
- Istvan Mezo, Summation of Hyperharmonic Numbers, arXiv:0811.0042 [math.CO], 2008.
- Index entries for transcendental numbers.
Programs
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Maple
evalf(Pi^4/72,120); # Muniru A Asiru, Sep 18 2018
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Mathematica
RealDigits[Pi^4/72,10,120][[1]] (* Harvey P. Dale, Feb 10 2013 *)
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PARI
Pi^4/72 \\ Michel Marcus, Jul 07 2015
Formula
Equals 20*Sum_{j >= 1} (2*j)^(-4) (see Gradsteyn and Ryzhik in Links section). - A.H.M. Smeets, Sep 18 2018
Equals Sum_{k>=1} A048272(k)/k^2. - Amiram Eldar, Jan 25 2024
Comments