The representation of an analytic function by general Laguerre series

If we select that branch of zi for which (z)i is real and positive when z < 0 then 3ΐ(z)& = H(rx)}i = b 2 gives the equation y 2 = 4 b + b 2 ) of the parabola which is the boundary of the above regions.The main result of this paper is the following.THEOREM A. In order that the function f(z) possess a Laguerre series of order a (a > -1) (or a general Laguerre series) which converges to it