A note on the values of zeta. From: Smarandache Notions Journal | Date: January 1, 2001| Author: Kim, Taekyun | COPYRIGHT 2001 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group.Copyright information

Carlitz considered the numbers [[eta].sub.k] (q) which are determined by

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These numbers [[eta].sub.k] (q) induce Carlitz's kth q-Bernoulli numbers [[eta].sub.k] (q) = [[beta].sub.k] as

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where we use the usual convention about replacing [[beta].sub.i] by [[beta].sub.i] (i [greater than or equal to] 0).

Now, we modify the abo...

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