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Max
  • Member for 1 year, 2 months
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17 votes
3 answers
968 views

One of the numbers $\zeta(5), \zeta(7), \zeta(9), \zeta(11)$ is irrational

10 votes
0 answers
214 views

Non trivial $f$ such that $\int_0^1 x^n f(x) dx=a_n\pi+b_n$

7 votes
6 answers
755 views

A question on Beta function

6 votes
2 answers
219 views

Finding a closed form for $\sum_{k=1}^\infty\sum_{n=k}^\infty\left(\frac{(-1)^k}{k^3\binom{n+k}{k}\binom{n}{k}}(\frac1{n^2}-\frac1{(n+1)^2})\right)$

6 votes
4 answers
373 views

Evaluate $\int_{0}^{\pi/2}x\sin^a (x) dx$, $a>0$

6 votes
3 answers
635 views

Closed form for zeros of a function

6 votes
3 answers
307 views

Closed form for $\sum_{n=1}^\infty \frac{1}{n(e^{2 n \pi}-1)}$

5 votes
0 answers
107 views

Closed form for $\sum_{n=1}^\infty x^{-\frac{2\pi}{n}} e^{-2\pi n}$

4 votes
1 answer
143 views

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

4 votes
1 answer
121 views

Asymptotic formula/closed form of $\sum_{r=0}^{n}\frac{(-1)^r\binom{n}{r}\log(n+r+1) }{n+r+1}$

4 votes
2 answers
360 views

Criteria for irrationality of Euler's constant

4 votes
0 answers
116 views

Asymptotic formula of a definite double integral

3 votes
0 answers
74 views

A question on Beukers proof of irrationality of $\zeta(3)$

3 votes
1 answer
145 views

Simplify $n$th derivative of $\frac{\log^3 x}{1-x}$

3 votes
0 answers
139 views

Prove that $-\int_{0}^{1}\frac{{\rm Li}_2(-x(1-x))}{x}\ dx=\frac{2}{5}\zeta(3)$

3 votes
1 answer
89 views

Closed form for $\sum_{n=1}^{\infty}\frac{(2\log\phi)^{2n+3}B_{2n}}{2n(2n+3)!}$

3 votes
1 answer
148 views

Series expansion of $\left(\frac{\sin x}{x}\right)^a$ at $x=0$

3 votes
1 answer
160 views

Expand $\cos^a x$ in terms of $\cos kx$, $\sin mx$

3 votes
1 answer
125 views

Closed form for an infinite sum

3 votes
0 answers
97 views

Closed form of series involving harmonic numbers

2 votes
1 answer
106 views

Simplified expression of $_2F_1(a,a;1+a;-1)$, $a<1$

2 votes
4 answers
121 views

Supremum of the function $f(x,y,z,u)=\frac{x(1-x)y(1-y)z(1-u)}{1-(1-xy)z}$

2 votes
0 answers
182 views

On a formula for Hypergeometric function $_3F_2(a,b,c;d,e;1)$

2 votes
2 answers
249 views

Partial fraction decomposition of $\frac{1}{(x(x+1)(x+2)...(x+n))^2}$

2 votes
1 answer
126 views

Asymptotic equality of $\frac{1}{n!}\frac{d^n}{dx^n}(x^n(1-x)^n) $

1 vote
0 answers
64 views

Necessary and sufficient condition for a number to be algebraic

1 vote
0 answers
92 views

Example of a specific polynomial

1 vote
0 answers
163 views

Asymptotic equality of an integral

1 vote
1 answer
205 views

Closed form of $\sum_{k=1}^{m} \frac{(-1)^{k+1} (m-k)\ c_{m-k}}{(2k+1)!}$

1 vote
1 answer
327 views

Closed form expression for an integral