Integral to Infinity of Cosine p x minus Cosine q x over x
Jump to navigation
Jump to search
Theorem
- $\ds \int_0^\infty \frac {\cos p x - \cos q x} x \rd x = \ln \frac q p$
where $p$ and $q$ are strictly positive real numbers.
Proof
This theorem requires a proof. In particular: probably contour integration You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 15$: Definite Integrals involving Trigonometric Functions: $15.38$