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Mathematics
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bob
  • Member for 1 year, 5 months
  • Last seen this week
  • University of Warwick
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First year at the University of Warwick studying Mathematics and Statistics. From Tokyo, Japan.

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13
Asymptotics of $\displaystyle{\sum_{i=0}^n\sqrt{i(n-i)}}$ as $n\to+\infty$
Aug 16, 2023
8
Trig Function with integration
Sep 16, 2023
8
Log-tangent integral using exponential generating function $\int_0^{\pi/2}x\log^n(\tan x)\,dx$
Jun 30, 2023
7
Improper Integrals as Riemann Sums and a Beautiful Limit $\lim_{n \to \infty}\frac{\sqrt[n]{n!}}{n}$
Jan 20, 2023
7
Encountered $\displaystyle{\sum_{k=1}^\infty\frac{(-1)^k\sin(kt)}{k}}$ while solving another integral
Sep 13, 2023
6
Asymptotics of $\displaystyle{\sum_{i=0}^n\sqrt{i(n-i)}}$ as $n\to+\infty$
Aug 18, 2023
5
Generalized log integral $\int_{0}^{\frac{\pi}{2}}\log(a+\sin(x))\,dx$
Jul 29, 2023
5
Showing convergence or divergance of the series $\sum_{k=1}^{\infty}\frac{\ln(k+1)-\ln(k)}{\sqrt{k+1}}$
Aug 14, 2023
5
How to find an asymptotic expansion of integral?
May 30, 2023
5
$\lim_{x\to 0} \left(\frac{\sec^2{x}}{x^2} - \cot^2{x}\right)$
Sep 17, 2023
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5
Implementing recurrence relation for an integral