On the evaluation of the integral \(\int_0^{\pi/4} \text{ln}(\cos^{m/n}\theta\pm \sin^{m/n}\theta)d\theta\) (Q1273309)
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scientific article; zbMATH DE number 1230030
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the evaluation of the integral \(\int_0^{\pi/4} \text{ln}(\cos^{m/n}\theta\pm \sin^{m/n}\theta)d\theta\) |
scientific article; zbMATH DE number 1230030 |
Statements
On the evaluation of the integral \(\int_0^{\pi/4} \text{ln}(\cos^{m/n}\theta\pm \sin^{m/n}\theta)d\theta\) (English)
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19 July 1999
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In this paper a procedure for the evaluation of the integrals \(\int^{\pi/4}_0\ln(\cos^{m/n}\vartheta\pm\sin^{m/n}\vartheta)d\vartheta\), \(m,n\) relatively prime positive integers, is given. Special cases of \(m\) and \(n\) are considered.
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Catalan constant
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Clausen function
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orthogonal polynomials
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logarithmic integrals
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