Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in and :
which he terms Ramanujan log-trigonometric integrals because they involve terms like
Ramanujan's nested radicals of 1/2.
The special case
was known to Euler.
Amazingly, the general integrals have closed forms
See alsoNested Radical
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ReferencesOloa, O. "Two Conjectures on Ramanujan Log-trigonometric Integrals." Unpublished manuscript. January 2010.
Referenced on Wolfram|AlphaRamanujan Log-Trigonometric
Cite this as:
Weisstein, Eric W. "Ramanujan Log-Trigonometric Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RamanujanLog-TrigonometricIntegrals.html