Calculation of Improper Integrals Using (nα)-Sequences

Abstract.

 We give a necessary and sufficient condition for the relation to hold as N → ∞. Here α is an irrational number, {x} denotes the fractional part of x and f is from a suitable class of functions with the property that lim _x→β+ f(x) = ±∞ or lim _x→β+ f(x) = ±∞ for a finite set of rational β ∈ [0,1].