Zeta Constant - The Riemann Zeta Function at 0 and 1

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:

    “The uses of travel are occasional, and short; but the best fruit it finds, when it finds it, is conversation; and this is a main function of life.”
    —Ralph Waldo Emerson (1803–1882)