A class of asymptotic relations for sine and cosine integrals

Abstract

In this paper, according to research results such as the asymptotic sums of a special class of sine and cosine series and the monotonicity of trigonometric series, we obtain some conclusions by establishing corresponding concepts compared with the discrete case and studying a class of asymptotic relations for special sine and cosine integrals. In addition, for the last theorem in the paper, we show that under the conditions {\mathrm{l}\mathrm{i}\mathrm{m}}_{t\to \mathrm{\infty }}\frac{f(t)}{\omega \left(t^{-1}\right)}=A and some assumptions on the modulus of continuity, these generalized monotonicity concepts are equivalent except for the second class of supremum bounded variation functions.

Keywords

Sine and cosine integral / monotonicity condition / asymptotic formula

References

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