Abstract
This paper offers a general expansion formula for oscillatory integrals of the form ∫ 0 1 x − α f ( x , { N x } ) d x \smallint _0^1{x^{ - \alpha }}f(x,\{ Nx\} )\,dx in which N is a large parameter, Nx denotes the fractional part of Nx, and α \alpha is a fixed real number in 0 > α > 1 0 > \alpha > 1 . Our formula is expressed in terms of some ordinary integrals with integrands containing periodic Bernoulli functions and the generalized Riemann zeta function.
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