I am in deadlock studyibg the pointwise and uniform convergence of the following series: $$\sum_{n=1}^{\infty}\frac{(n+1)^n-n^n}{n!}x^{n^n}$$
Maybe should I handle it as a power series? But how? Any tips?
2026-02-23 12:36:05.1771850165
Pointwise and uniform convergence $\sum_{n=1}^{\infty}\frac{(n+1)^n-n^n}{n!}x^{n^n}$
42 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in POWER-SERIES
- Conditions for the convergence of :$\cos\left( \sum_{n\geq0}{a_n}x^n\right)$
- Power series solution of $y''+e^xy' - y=0$
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Pointwise and uniform convergence of function series $f_n = x^n$
- Divergence of power series at the edge
- Maclaurin polynomial estimating $\sin 15°$
- Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$
- How to I find the Taylor series of $\ln {\frac{|1-x|}{1+x^2}}$?
- Convergence radius of power series can be derived from root and ratio test.
- Recognizing recursion relation of series that is solutions of $y'' + y' + x^2 y = 0$ around $x_0 = 0$.
Related Questions in UNIFORM-CONVERGENCE
- Comparing series by absolutes of summands
- proving continuity claims
- uniform or dominated convergence of sequence of functions which are bounded
- Uniform convergence of products
- Proof of uniform convergence of functional series
- I can't understand why this sequence of functions does not have more than one pointwise limit?
- If $g \in L^1$ and $f_n \to f$ a.e. where $|f_n| \leq 1$, then $g*f_n \to g*f$ uniformly on each compact set.
- Uniform convergence of a series depending on $\alpha ,\beta$
- Analysis Counterexamples
- Prove that the given series of functions is continuously differentiable.
Related Questions in POINTWISE-CONVERGENCE
- I can't understand why this sequence of functions does not have more than one pointwise limit?
- Typewriter sequence does not converge pointwise.
- Fourier Series on $L^1\left(\left[0,1\right)\right)\cap C\left(\left[0,1\right)\right)$
- Analyze the Pointwise and Uniform Convergence of: $f_n(x) = \frac{\sin{nx}}{n^3}, x \in \mathbb{R}$
- Uniform Convergence of the Sequence of the function: $f_n(x) = \frac{1}{1+nx^2}, x\in \mathbb{R}$
- Elementary question on pointwise convergence and norm continuity
- Pointwise and Uniform Convergence. Showing unique limit.
- A sequence $f_k:\Omega\rightarrow \mathbb R$ such that $\int f_k=0 \quad \forall k\in \mathbb N $ and $\lim\limits_{k\to\infty} f_k \equiv1$.
- Show that partial sums of a function converge pointwise but not uniformly
- example of a sequence of uniformly continuous functions on a compact domain converging, not uniformly, to a uniformly continuous function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?