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where m is a positive integer and r is real. Several authors (e.g. see [2], [5], and [6] and the references there given) have derived identities for >?n n a(n)(x -Ajq where q is real. On the contrary, only in a few special cases have identities been given for >An <, a(n) logq (x/An). In this paper we derive identities for the aforementioned sum when q is a nonnegative integer and q is a Dirichlet series belonging to the same class as that studied in [2]. We conclude with several examples involving well-known arithmetical functions. Throughout the sequel we let s=a+it with a and t both real. If c is real, we denote the integral f C i+ by S(c) The summation sign 2 appearing with no indices will always mean _n=1 . J,(x) always denotes the usual Bessel function of order v. c, cn and c', 0 _ n < oo, always denote constants, not necessarily the same with each occurrence. Also, q always denotes a nonnegative integer.

Identities involving the coefficients of a class of Dirichlet series. IV