The mean convergence of non-harmonic series

The Convergence of Smarandache Harmonic Series

harmonic series. The article shows that the series I-,lis divergent and n2!2 S-(n) n 1 studies from the numerical point of view the sequence an = I-2-. -In(n). 1=2 S (1)

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Mean Convergence of Vector–valued Walsh Series

Given any Banach space X, let L X 2 denote the Banach space of all measurable functions f : [0, 1] → X for which f 2 := 1 0 f (t) 2 dt

On the Convergence of the Euler Harmonic Series

The aim oj this article is to study the convergence oj the Euler harmonic series. Firstly, the results concerning the convergence oj the Smaralldache and Erdos harmonic junctions are reviewed Secondly, the Euler harmonic series is proved to be convergent jor a> I, and divergent otherwise. Finally, the slims of the Euler harmonic series are given

The Mean Convergence of Orthogonal Series of Polynomials.