On the Uniform Approximation of a Class of Analytic Functions by Bruwier Series Original Research Article

For a class of analytic functions f(z) defined by Laplace–Stieltjes integrals the uniform convergence on compact subsets of the complex plane of the Bruwier series (B-series) ∑∞n=0 λn(f) (z−nc)nn!, λn(f)=f(n)(nc)+cf(n+1)(nc), generated by f(z) and the uniform approximation of the generating function f(z) by its B-series in cones |arg z|⩽ϕ<π2 is shown.