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Given a commutative ring with identity R, many different and interesting operations can be defined over the set $$H_R$$ HR of sequences of elements in R. These operations can also give $$H_R$$ HR the structure of a ring. We study some of these operations, focusing on the binomial convolution product and the operation induced by the composition of exponential generating functions. We provide new...
We study some properties and perspectives of the Hurwitz series ring $$H_R[[t]]$$ HR[[t]] , for an integral domain R, with multiplicative identity and zero characteristic. Specifically, we provide a closed form for the invertible elements by means of the complete ordinary Bell polynomials, we highlight some connections with well–known transforms of sequences, and we see that the Stirling transforms...
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