Riesz mean

In mathematics, the Riesz mean is a certain mean of the terms in a series. They were introduced by Marcel Riesz in 1911 as an improvement over the Cesàro mean. The Riesz mean should not be confused with the Bochner–Riesz mean or the Strong–Riesz mean.

Given a series ${\displaystyle \{s_{n}\}}$, the Riesz mean of the series is defined by

Sometimes, a generalized Riesz mean is defined as

Here, the ${\displaystyle \lambda _{n}}$ are sequence with ${\displaystyle \lambda _{n}\to \infty }$ and with ${\displaystyle \lambda _{n+1}/\lambda _{n}\to 1}$ as ${\displaystyle n\to \infty }$. Other than this, the ${\displaystyle \lambda _{n}}$ are otherwise taken as arbitrary.

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