Relations between Certain Sums and Integrals Concerning Power Series with Hadamard Gaps
D. Gnuschke · Complex Variables Theory and Application An International Journal · 1984
Let ∑ kakznλ be analytic for . It is shown that if f has Hadamard gaps , i.e. then the finiteness of essentially equivalent to that of where R is a radius of . More precisely, the sum is finite if the integral is, even for an arbitrary curve instead of a radius with no condition whatever on α. For the other direction the restriction α> –1 is necessary.