We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.

The purpose of this paper is twofold. In the first section we provide sufficient conditions for the divisibility of the class number of certain algebraic number fields by prime powers and applications thereof. We were initially inspired in this regard by Watabe [ 111, wherein some of the results are false thereby leading to the above. In the second section we generalize Fermat’s well-known “two...

While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.

In this comment, I extend Cavalcanti and Nosal’s (2010) framework to include the case of perfectly divisible money and unrestricted money holdings. I show that when trade takes place in Walrasian markets, counterfeits circulate and the Friedman rule is still optimal.

We determine the p-exponent in many of the coefficients of `(x), where `(x) is the power series for log(1+x)/x and t is any integer. In our proof, we introduce a variant of multinomial coefficients. We also characterize the power series x/ log(1 + x) by certain zero coefficients in its powers. 1. Main divisibility theorem The divisibility by primes of the coefficients in the integer powers `(x)...

The main idea is to consider generalized binomial coefficients that are formed from an arbitrary sequence C, as shown in (3) below. We will isolate a property of the sequence C that guarantees the existence of a theorem like Kummer’s, relating divisibility by prime powers to carries in addition. A special case of the theorem we shall prove describes the prime power divisibility of Gauss’s gener...