# hammood

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1526
bio website location Damascus, Syria age member for 1 year, 6 months seen 15 hours ago profile views 483

interested in math and modern physique

# 65 Questions

 42 Is there a function with the property$f(n)=f^{(n)}(a)$ 22 Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$ 18 Finding the fraction $\frac{a^5+b^5+c^5+d^5}{a^6+b^6+c^6+d^6}$ when knowing the sums $a+b+c+d$ to $a^4+b^4+c^4+d^4$ 12 integral of $\int \limits_{0}^{\infty}\frac {\sin (x^n)} {x^n}dx$ 11 closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$

# 2,310 Reputation

 +10 Why does the series $\sum_{n=1}^\infty\frac1n$ not converge? +5 closed form for $\int_0^1x^{a+1}(1-x^2)^bJ_a(cx)dx$ +10 Expanding Limit $\lim_{n\to\infty}\sum_{k=1}^n\frac{1}{n^2\log(1+\frac{k^2}{n^2})}=\frac{{\pi}^2}{6}$ +5 show that $\int_{0}^{\infty } \frac{\sin (ax)}{x(x^2+b^2)^2}dx=\frac{\pi}{2b^4}(1-\frac{e^{-ab}(ab+2)}{2})$

 12 Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ 7 Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$ 5 Is there any formula for summation? 4 Surprising identities / equations 4 Compute $\int_{-\infty}^{\infty} \frac{x^2}{(1+x^2)^2} dx$

# 59 Tags

 37 calculus × 34 12 recreational-mathematics 17 integration × 26 9 real-analysis × 4 17 limits × 11 7 algebra-precalculus × 5 12 infinite-product × 2 7 trigonometry × 4 12 problem-solving 6 summation × 8

# 22 Accounts

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