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Riemann zeta function for nonnegative even integers. The Riemann zeta function for negative even integers is 0 (those are the trivial zeros of the Riemann zeta function). The Riemann zeta function for nonnegative even integers is given by (note that is the only rational number for nonnegative even integers) where are the Bernoulli numbers.
Purpose: The purpose of Zeta Tau Alpha is the intensifying of friendship, the fostering of a spirit of love, the creating of such sentiments, the performing of such deeds, and the moulding of such opinions as will be conducive to the building up of a purer and nobler womanhood in the world.