New posts in real-analysis

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

real-analysis integration trigonometry harmonic-numbers polylogarithm

Is $\int_{\mathbb{R}^2} e^{-u} \Delta u < \infty$?

real-analysis integration

Rudin Theorem $1.11$

real-analysis analysis order-theory supremum-and-infimum upper-lower-bounds

Solve the equation: $e^x=mx^2$

Differentiability of Convolutions

Cesaro summable implies that $c_{n}/n$ goes to $0$

real-analysis analysis fourier-analysis fourier-series

Does $\mu^{}(E)=1$ imply $\mu^{}(E^{c})=0$ when $\mu$ is an outer measure and the measure of the space is $1$

Prove $\left(\frac{n+1}{\text{e}}\right)^n<n!<\text{e}\left(\frac{n+1}{\text{e}}\right)^{n+1}$ [closed]

calculus real-analysis inequality

Writing Integrals using Differential Forms

real-analysis integration multivariable-calculus differential-forms

How prove that $xyz+\sqrt{x^2y^2+y^2z^2+x^2z^2}\ge \frac{4}{3}\sqrt{xyz(x+y+z)}$

real-analysis inequality radicals substitution uvw

A function is $L^2$-differentiable if and only if $\xi\widehat{f}(\xi) \in L^2$.

real-analysis functional-analysis fourier-analysis

Sums in $\mathbb N^3$

real-analysis sequences-and-series convergence-divergence

Does there exist a function $f: \mathbb{R} \to \mathbb{R}$ that is differentiable only at $0$ and at $\frac{1}{n}$, $n \in \mathbb{N}$?

calculus real-analysis derivatives examples-counterexamples

Sturm-Liouville problem and periodic boundary conditions

real-analysis analysis functional-analysis operator-theory spectral-theory

Prove that the following three metric space/subsequence boundedness conditions are equivalent.

real-analysis metric-spaces

Continuous functions of $(0,1)$ form a metric space

real-analysis metric-spaces

Proof using asymptotic notion with fractional function

real-analysis asymptotics

Integral and mean value theorem question

real-analysis integration

if $|f(n+1)-f(n)|\leq 2001$, $|g(n+1)-g(n)|\leq 2001$, $|(fg)(n+1)-(fg)(n)|\leq 2001$ then $\min\{f(n),g(n)\}$ is bounded

real-analysis functions

Proof of $(0,1)$ is not compact with usual metric.

real-analysis general-topology