New posts in real-analysis

Is the closed form of $\int_0^1 \frac{x\ln^a(1+x)}{1+x^2}dx$ known in the literature?

real-analysis calculus integration reference-request polylogarithm

Weak* convergence in $L^\infty$ and the strong convergence in $L^2$ of a mollification?

real-analysis functional-analysis lp-spaces convolution weak-convergence

It is easy to show that $S_m=\sum_{n=1}^\infty \frac{n}{2^n + m}$ converges for any natural$\ m$, but what is its value?

calculus real-analysis sequences-and-series limits proof-writing

Modified Doob's $L^1$ inequality

real-analysis probability inequality stochastic-processes

My proof that sum of convergent sequences converges to sum of limits

real-analysis sequences-and-series limits solution-verification

If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

real-analysis sequences-and-series uniform-convergence

How do i evaluate this sum $\sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2n!}$?

real-analysis sequences-and-series summation

Why differentiability implies continuity, but continuity does not imply differentiability?

real-analysis derivatives continuity examples-counterexamples

To find the minimum value of $|z+1|+|z-1|+|z-i|$ where $z\in \Bbb C$.

calculus real-analysis complex-analysis optimization

finite polynomials satisfy $|f(x)|\le 2^x$

real-analysis polynomials contest-math nonlinear-optimization

Inequality for nonegative real numbers

real-analysis inequality holder-inequality

Find all $z$ such that $e^{2\pi i z}=1$

real-analysis calculus complex-analysis complex-numbers

How to solve $(y)^{y'}=(y')^{y+c},c \in \mathbb{R}$

calculus real-analysis ordinary-differential-equations change-of-variable

How can I show the sets are open? (The set of rational numbers $\mathbb{Q}$ is not a connected topological space)

real-analysis general-topology rational-numbers

Proving f is a Lipschitz continuous function. (Real analysis)

real-analysis continuity

Show that for every set $A \subset \mathbb R^n$ lebesgue measurable $\int_{A} f_n dx\rightarrow \int_{A} f dx.$ [closed]

real-analysis measure-theory lebesgue-integral lebesgue-measure measurable-functions

Elliptic Integrals & Gamma Functions of Rational values.

real-analysis integration sequences-and-series multivariable-calculus elliptic-integrals

Sum of $\sum_{n \geq 1} \frac{(\ln x +1)^n}{n^n}$

calculus real-analysis sequences-and-series summation power-series

Can we approximate a vector field on the plane with non-vanishing vector fields in $L^2$?

real-analysis differential-topology lp-spaces vector-fields singularity-theory

There exist meager subsets of $\mathbb{R}$ whose complements have Lebesgue measure zero

real-analysis general-topology measure-theory baire-category