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Date: 15-5-2018
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Date: 23-5-2019
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Date: 15-5-2018
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Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in and
:
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(1) |
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(2) |
which he terms Ramanujan log-trigonometric integrals because they involve terms like Ramanujan's nested radicals of 1/2.
The special case
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(3) |
was known to Euler.
Amazingly, the general integrals have closed forms
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(4) |
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(5) |
for .
REFERENCES:
Oloa, O. "Two Conjectures on Ramanujan Log-trigonometric Integrals." Unpublished manuscript. January 2010.
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دراسة: عدم ترتيب الغرفة قد يدل على مشاكل نفسية
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علماء: تغير المناخ تسبب في ارتفاع الحرارة خلال موسم الحج
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جهود مكثفة وطباعة عشرات الآلاف من المنشورات .. استعدادات العتبة العلوية المقدسة لعيد الغدير الأغر
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