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Some generating functions of the Riemann zeta function

. In this survey paper, functional relations between some generating functions of the Riemann zeta function are formulated. These generating functions themselves are zeta-functions (Bessel type, conﬂuent-hypergeometric type and hypergeometric type), introduced by M. Katsurada and the author. The explicit formula of the special values of these zeta functions at non-positive integers are also given.