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vesszabo's user avatar
vesszabo's user avatar
vesszabo
  • Member for 13 years, 4 months
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  • Hungary
47 votes

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

13 votes
Accepted

For holomorphic $f$, $f(\frac{z}{2})= \frac{1}{2}f(z) \Longrightarrow f(z) = z$

12 votes

How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$

11 votes

How prove this $f(n)\le f(n+1)$ where $f(n)=\sum_{k=1}^{n}\frac{n}{n^2+k^2}$

9 votes

Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor

8 votes

Fractional calculus in complex analysis

7 votes

How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$

6 votes
Accepted

Definite integral involving Fresnel integrals

6 votes

How prove this inequality $ 1-\cos (xy) \le\int_0^xf(t) \sin {(tf(t))}dt + \int_0^y f^{-1}(t) \sin{(tf^{-1}(t))} dt .$

6 votes

How to find the limit $x_n=\frac{(a)(a+1)(a+2)..(a+n)}{(b)(b+1)(b+2)..(b+n)}$

5 votes

Is this definite integral really independent of a parameter? How can it be shown?

4 votes

How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$

4 votes

A young limit $\lim_{n\to\infty} \frac{{(n+1)}^{n+1}}{n^n} - \frac{{n}^{n}}{{(n-1)}^{n-1}} =e$

4 votes

Beyond Calculus?? Integral Convergence using Measure Theory & Real Analysis

3 votes

Integrating $\int_{-1}^{1}(1+x)^m(1-x)^ndx$

3 votes

Study continuity of this function

3 votes

Approximating continuous functions with polynomials

3 votes

$\epsilon>0$ there is a polynomial $p$ such that $|f(x)-e^{-x}p|<\epsilon\forall x\in[0,\infty)$

3 votes

Proving that $\sin x \ge \frac{x}{x+1}$

3 votes
Accepted

Prove that the even (odd) degree Legendre polynomials are even > (odd) functions of $t$.

3 votes

Prove that $\frac{{a}^{2}}{b-1}+\frac{{b}^{2}}{a-1}\geq8$

3 votes
Accepted

$(x^n-x^m)a=(ax^m-4)y^2$ in positive integers

3 votes

Why is it legit to evaluate $\lim_{x\rightarrow 1} \frac{(x-1)(x+1)}{x-1}$ by cancelling common factors?

3 votes

Inequality of weights on a graph

3 votes
Accepted

Optimization with non-negativity and norm constraint

3 votes

On Jacobi Polynomial

2 votes
Accepted

How do I evaluate this limit with an integral function?

2 votes

Solving second order linear differential equations with non-constant coefficients

2 votes

How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?

2 votes

What is the Modulus of a Matrix?