Sum of Zeta Constants
The following sums can be derived from the generating function:
where is the digamma function.
Series related to the Euler–Mascheroni constant (denoted by γ) are
and using the principle value (which of course effects only the value at 1) these formulae can be stated nicer as
and show that they "live" only because the principle value of .
Read more about this topic: Zeta Constant
Famous quotes containing the words sum of and/or sum:
“[M]y conception of liberty does not permit an individual citizen or a group of citizens to commit acts of depredation against nature in such a way as to harm their neighbors and especially to harm the future generations of Americans. If many years ago we had had the necessary knowledge, and especially the necessary willingness on the part of the Federal Government, we would have saved a sum, a sum of money which has cost the taxpayers of America two billion dollars.”
—Franklin D. Roosevelt (1882–1945)
“To sum up:
1. The cosmos is a gigantic fly-wheel making 10,000 revolutions a minute.
2. Man is a sick fly taking a dizzy ride on it.
3. Religion is the theory that the wheel was designed and set spinning to give him the ride.”
—H.L. (Henry Lewis)