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Published online by Cambridge University Press: 24 October 2008
In the theory of functions of a complex variable a positive quantity g(r), denned in terms of a circle |z| = r, can often be estimated by means of another similar quantity f(R) denned in terms of a circle |z| = R with R > r. Inequalities of the form
arise in this connexion. Putting R = r + h we have for every h > 0
.