On the relation of Cesàro summability to generalized (F α, q) summability
Copyright policy )On the relation of Cesàro summability to generalized (F α, q) summability
Standard special cases of the sequence-to-functionF (a, q)-transform of Meir4 admit of a more general, essentially more refined, characterization as theFk (a, q)-transform of the sequel, adapted from one of Faulhaber’s.1 The theorem proved,viz., that (Fa, qk) summability for sequences, corresponding to the latter transform, includes Cesaro summability of a positive integer order with a certain rapidity, applies to the standard special cases of (Fα, q) and (Fa, qk) summabilities which are, in famiiar notation, summabilities(Ep), (Tα), (Sβ), (Va) and (Bα, γ) whose further special case (B1, 1) is Borel summability. The special cases of (V1/2) and Borel summabilities go back to Hyslop.3
Abel, Borel and power series methods, Cesàro, Euler, Nörlund and Hausdorff methods, Special methods of summability, Function-theoretic methods (including power series methods and semicontinuous methods) for summability, Inclusion and equivalence theorems in summability theory
Abel, Borel and power series methods, Cesàro, Euler, Nörlund and Hausdorff methods, Special methods of summability, Function-theoretic methods (including power series methods and semicontinuous methods) for summability, Inclusion and equivalence theorems in summability theory
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