Ramanujan Log-Trigonometric Integrals
المؤلف:
Oloa, O
المصدر:
"Two Conjectures on Ramanujan Log-trigonometric Integrals." Unpublished manuscript. January 2010.
الجزء والصفحة:
...
25-8-2018
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Ramanujan Log-Trigonometric Integrals
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
 |
(3)
|
was known to Euler.
Amazingly, the general integrals have closed forms
for 
.
REFERENCES:
Oloa, O. "Two Conjectures on Ramanujan Log-trigonometric Integrals." Unpublished manuscript. January 2010.
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