Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

Let $\gamma: \lbrack -1, 1 \rbrack \rightarrow R^n$ be an odd curve. Set $$H_\gamma f(x) = PV \int f(x - \gamma(t)) (dt/t)$$ and $$M_\gamma f(x) = \sup h^{-1} \int^h ...

SINCE the publication of Prof. Zygmund's “Trigonometric Series” in 1935, there has been considerable demand for another book dealing with trigonometric integrals. Prof. Titchmarsh's book meets this ...