real analysis related issues & queries in MathXchanger

Crazy incredible log equation

real-analysis logarithms finance
Updated August 23, 2019 07:20 AM

Two cool sums: Compute $\sum_{n=1}^\infty (-1)^{n}\frac{H_{2n+1}}{(2n+1)^3}$ and $\sum_{n=1}^\infty (-1)^{n}\frac{H_{2n+1}^{(2)}}{(2n+1)^2}$

integration sequences-and-series definite-integrals harmonic-analysis polygamma
Updated August 23, 2019 07:20 AM

How can one use Mean Value Theorem to prove the following equality?

real-analysis functions
Updated August 23, 2019 07:20 AM

If $f$ is differentiable at $a$, then $\lim_{x\rightarrow a}f(x)$ exists.

calculus analysis
Updated August 23, 2019 06:20 AM

problem from real analysis

real-analysis sequences-and-series
Updated August 23, 2019 06:20 AM

Real analysis problem from sequences?

real-analysis sequences-and-series cauchy-sequences
Updated August 23, 2019 05:20 AM

Questions about sets in Apostol's analysis

real-analysis general-topology
Updated August 23, 2019 03:20 AM

Convexity of logarithmic function with inner product and $\ell_1$-norm

vector-spaces convex-analysis convex-optimization hessian-matrix
Updated August 23, 2019 03:20 AM

Closures under different inner products and the injectivity

general-topology functional-analysis
Updated August 23, 2019 03:20 AM

Packing number of inverse image of a function

real-analysis geometry differential-geometry metric-spaces geometric-topology
Updated August 23, 2019 03:20 AM

How to prove it is a $\sigma-$ ring

real-analysis measure-theory singular-measures
Updated August 23, 2019 02:20 AM

Evaluate $\lim_{n\to \infty}\frac{n+n^2+n^3+...+n^n}{1^n+2^n+3^n+...+n^n}$

real-analysis calculus sequences-and-series limits riemann-integration
Updated August 23, 2019 02:20 AM

"Steady-state" of Error function using Fourier Transform

fourier-analysis fourier-transform
Updated August 23, 2019 02:20 AM

Can we define a metric on R such that all sequences are convergent?

real-analysis metric-spaces
Updated August 23, 2019 01:20 AM

error estimation for the Fourier series of the fractional part of $x$

real-analysis fourier-analysis fourier-series
Updated August 23, 2019 01:20 AM

Domain of composition of function

real-analysis analysis
Updated August 23, 2019 01:20 AM

Geometric Interpretation of Laplace's Equation

complex-analysis analysis harmonic-functions
Updated August 23, 2019 01:20 AM

Functional calculus for diagonalisable unbounded operators

functional-analysis hilbert-spaces differential-operators unbounded-operators
Updated August 23, 2019 00:20 AM

Analysis of multi-vectors

vector-analysis clifford-algebras
Updated August 22, 2019 23:20 PM

measureability of a function and its relation to the completion of the measure

real-analysis measurable-functions
Updated August 22, 2019 23:20 PM

$d/dx$ is not continuous in $L^2$

real-analysis pde
Updated August 22, 2019 23:20 PM

Proving that $G(z+1)=\Gamma (z)G(z)$

complex-analysis analysis gamma-function
Updated August 22, 2019 22:20 PM

Integral with respect to spectral measure

functional-analysis measure-theory spectral-theory unbounded-operators self-adjoint-operators
Updated August 22, 2019 22:20 PM

If $f:R \to R$ is a countinous function and there are $a \geq 0$ and $b \geq 0$ such that $\|f(x)\| \leq a\|x\| + b$ then $f$ is uniformly countinous.

real-analysis uniform-continuity
Updated August 22, 2019 21:20 PM

Does $\lim_{x\to 1^-}\sum_{n=0}^\infty a_n x^n\neq\infty$ implies $-\infty<\liminf\sum_{n=0}^N a_n\le\limsup\sum_{n=0}^N a_n<+\infty$?

real-analysis sequences-and-series power-series summation-method
Updated August 22, 2019 21:20 PM

Let [$c_n$]{for $n$ from $0$ to $+\infty$} be a sequence of real numbers.

real-analysis sequences-and-series limits
Updated August 22, 2019 21:20 PM

(Another) Possible Representations of function (which already exist in terms of integral)

functional-analysis analysis analytic-functions
Updated August 22, 2019 21:20 PM

Pull-back property $f^*(dx^i)=df^i$

analysis differential-geometry differential-forms multilinear-algebra exterior-algebra
Updated August 22, 2019 20:20 PM

Continous choice of elements in the kernel of linear maps

linear-algebra analysis multivariable-calculus differential-geometry continuity
Updated August 22, 2019 20:20 PM

compact convergence on a non-compact metric space implies continuity

real-analysis proof-verification metric-spaces uniform-convergence
Updated August 22, 2019 19:20 PM

Question on Cauchy Estimates.

complex-analysis estimation cauchy-integral-formula
Updated August 22, 2019 19:20 PM

If $f$ is increasing on some infinite interval, then $f$ is positively unbounded.

real-analysis proof-verification
Updated August 22, 2019 19:20 PM

$\int_{0}^{\infty} \frac{\cos x - e^{-x^2}}{x} \ dx$ Evaluate Integral

calculus real-analysis integration improper-integrals
Updated August 22, 2019 19:20 PM

Is the set of all convex functions metric space?

metric-spaces convex-analysis
Updated August 22, 2019 18:20 PM

What's the "limit" in the definition of Riemann integrals?

real-analysis integration limits riemann-integration nets
Updated August 22, 2019 18:20 PM

Solving a linear system in matrix notation

linear-algebra vector-analysis numerical-linear-algebra matrix-calculus tensors
Updated August 22, 2019 17:20 PM

Generalizing reflection principle to arbitrary domains

complex-analysis
Updated August 22, 2019 17:20 PM

What's the supremum of $\{x \in F: -2 < x \le 2\}$?

real-analysis proof-verification real-numbers
Updated August 22, 2019 17:20 PM

Calculate $\sum_{n \in A} 2^{-n}$

real-analysis discrete-mathematics summation
Updated August 22, 2019 16:20 PM

How to extend continous function from $S^1\to S^1$ to $D^2\to D^2$ continously

real-analysis general-topology algebraic-topology
Updated August 22, 2019 16:20 PM

Sup norm of vector-valued function

functional-analysis
Updated August 22, 2019 16:20 PM

Proving that $\mathbb{R}_K$ is connected with the topology $\tau$

general-topology analysis
Updated August 22, 2019 16:20 PM

Evaluate $\int_{0}^{\frac{\pi}{4}}\tan xdx $ using idea of Riemann Sum

real-analysis calculus integration definite-integrals
Updated August 22, 2019 16:20 PM

Prove that $\sum_{i=0}^{m_n} \Delta x_i^n\varepsilon _{i,n}(\Delta x_{i}^n)\to 0$ when $n\to \infty $.

real-analysis
Updated August 22, 2019 16:20 PM

Study the convergence of the series

real-analysis
Updated August 22, 2019 15:20 PM

Unique time reachability for two symmetric ODE

real-analysis ordinary-differential-equations examples-counterexamples
Updated August 22, 2019 15:20 PM

Generalizing a function that operates on functions

calculus functional-analysis functions smooth-functions
Updated August 22, 2019 15:20 PM

can a function from (0,1) to (0,1] be 1-1 and onto

real-analysis
Updated August 22, 2019 14:20 PM

Steady-state of a system and Fourier Transform

fourier-analysis fourier-transform
Updated August 22, 2019 13:20 PM

Is it possible to interchange order of supremum and supremum?

real-analysis
Updated August 22, 2019 13:20 PM

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