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Template:Sequence of the Day for October 7

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Intended for: October 7, 2013

Timetable

  • First draft entered by Alonso del Arte on March 31, 2012
  • Draft reviewed by Daniel Forgues on October 6, 2012
  • Draft to be approved by September 7, 2013
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A082020: Decimal expansion of
15
 π 2
.
1.519817754635...

This is one of those numbers which can be expressed both as an infinite sum and as an infinite product:

n   = 1
  
| μ (n) |
n  2
 = 
15
π  2
 ,
p
p prime
p
p prime
  
1 +
1
p  2
 = 
15
π  2
 ,
where
μ (n)
is the Möbius function and the infinite product is over all primes. Yet another expression for this number is
ζ  (2)
ζ  (4)
=
π 2 / 6
π 4 / 90
, where
ζ  (s)
is the Riemann zeta function.