The Integration of Functions of a Single Variable

a₁ absolute convergence algebraical function apply arithmetic arithmetic means ax²+2bx+c B₂ Bohr Bois-Reymond Borel Bromwich Cesaro's coefficients consider curve deduce defined denote differentiation divergent elementary function equation example exponential expressed factor finite number finite order follows formula G. H. Hardy generalisation given half-plane Hence increase of ƒ increasing function infinity of values integral function J₁ L-function of order Landau Lemma limit Lindelöf Lindelöf's Theorem log log logarithmic logarithmic means logarithmico-exponential Math mean value theorem method obtain ordinary Dirichlet's series polynomial positive number power series proof proved rational function result Riesz scales series is convergent series is summable sufficiently large values suppose tends to infinity Theorem 17 Theorem 41 Theorems 23 theory true typical means uniformly convergent variable write y₁ λη