Integral to Infinity of Sine p x Cosine q x over x/Mistake
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Source Work
1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables
- Chapter $15$: Definite Integrals
- Definite Integrals involving Trigonometric Functions: $15.34$
This mistake can be seen in the edition as published by Schaum: ISBN 0-07-060224-7 (unknown printing).
Mistake
- $\ds \int_0^\infty \frac {\sin p x \cos q x} x \rd x = \begin {cases} 0 & : p > q > 0 \\
\dfrac \pi 2 & : 0 < p < q \\ \dfrac \pi 4 & : p = q > 0 \end {cases}$
Correction
As demonstrated in Integral to Infinity of $\dfrac {\sin p x \cos q x} x$, this is incorrect.
It should be:
- $\ds \int_0^\infty \frac {\sin p x \cos q x} x \rd x = \begin {cases} \dfrac \pi 2 & : p > q > 0 \\
0 & : 0 < p < q \\ \dfrac \pi 4 & : p = q > 0 \\ \end {cases}$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 15$: Definite Integrals involving Trigonometric Functions: $15.34$