On Euler's formula by which convergent series are made more rapidly convergent

On Absolutely Convergent Dirichlet Series

satisfying zZ\ \^A < °°, if and only if f is) is bounded away from zero in the half-plane 0-3:0. This discovery amounts to a determination of the spectrum of the Banach-algebra element associated with fis), and it thus makes available for the theory of ordinary Dirichlet series the well-known theorem of Gelfand on analytic functions of Banach-algebra elements (see §24D of [7]) and its generaliz...

On Cantor's Series with Convergent

On Faster Convergent Infinite Series

Recommended by Laszlo Toth Suffcient conditions, necessary conditions for faster convergent infinite series, faster τ-convergent infinite series are studied. The faster convergence of infinite series of Kummer's type is proved. Copyright q 2008 Dušan Hoí y et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distributi...

Note on Absolutely Convergent Dirichlet Series

is it true that \f(s)\ s^k>0 for cr^O implies that (/(s))-1 is also of the form (1)? In this note, an affirmative answer is supplied.3 Let P be the semigroup of positive integers under multiplication, and let h(P) be the class of all complex functions a on P, a= {an}»~i, for which ||a|| = y^°-i \an\ is finite. We obtain a commutative Banach algebra by defining (aa)n = aan for complex a, (a+b)n ...

A Rapidly Convergent Descent Method for Minimization

27 information is used. A choice then has to be made as to which is the most eecient option. Acknowledgments. We are grateful to the referees for their useful comments. We thank Robert Michael Lewis for his valuable suggestions on how best to present this material, particularly the results given in x7. Mathematical models for the predictive value of early CA125 serum levels in epithelial ovaria...