The Riemann Zeta Function At 0 and 1
At zero, one has
At 1 there is a pole, so ΞΆ(1) is not defined but the left and right limits are:
and
and because it is a pole of 1st order its principle value exists and is .
Read more about this topic: Zeta Constant
Famous quotes containing the word function:
“If the children and youth of a nation are afforded opportunity to develop their capacities to the fullest, if they are given the knowledge to understand the world and the wisdom to change it, then the prospects for the future are bright. In contrast, a society which neglects its children, however well it may function in other respects, risks eventual disorganization and demise.”
—Urie Bronfenbrenner (b. 1917)