## Tagged Questions

0answers
37 views

### Series expansion with remaining $log n$

Hi, I'm studying the asymptotic behavior $(n \rightarrow \infty)$ of the following formula, where $k$ is a given constant. $$\frac{1}{n^{k(k+1)/(2n)}(2kn−k(1+k) \ln n)^2}$$ I'm …
0answers
68 views

### Two Series Questions [closed]

1) iF $f(x) = x^2 +x$, find the taylor series for f centered at a = 2. 2)what is the sum from 1 to infinity of $(.95)^n$ I got these questions wrong on my last test, and I'm not …
1answer
121 views

### Inequality of Partial Taylor Series

Hi, For a given $\theta < 1$, and $N$ a positive integer, I am trying to find an $x > 0$ (preferably the smallest such $x$) such that the following inequality holds: \sum_{k …
0answers
55 views

### Taylor expansion of a one-parameter transformation

If we have a $\phi: \mathbb{R} \times \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}$, $\phi = \phi(t, \mathbf{q},\alpha)$ one-parameter group of infinitesimal transformation which …
0answers
50 views

### Find a bounded function with a supporting point

Given, $g(Z)=\operatorname{tr}\phi(Z)$, where $\phi(Z)= Z^T\left( \operatorname{diag}(ZZ^T\mathbf{1}) - ZZ^T\right) Z$ where $Z$ is a real rectangular matrix with more rows than co …
1answer
168 views

### A question about approximation of Real analytic functions

Define $B$ to be the set of functions $f:[0,1]\rightarrow \mathbb{R}$ for which there exists a dense set $C\subset [0,1]$ of computables numbers and an algorithm $F$ such that for …
0answers
75 views

### Calculating entropy of adjacency matrix using eigenvalue decomposition?

How to calculate entropy using the eigenvalues when the eigenvalues are negative? http://mathoverflow.net/questions/102569/is-there-a-simple-relation-between-the-entropy-of-a-mat …
2answers
112 views

### Taylor expansion convergence relation to power-spectrum

Is there some connection between the power-spectrum of a real function $f:\mathbb{R}\to\mathbb{R}$ (that is, its Fourier transform) and the convergence radius of its Taylor expansi …
0answers
128 views

### The bound on derivatives of a function [closed]

Let $f(x)$ be a smooth function from $\mathbb{R}$ to $\mathbb{R}$. Is there any way to find an upper bound (any bound, not necessary supremum) on The $n^{th}$ derivative of $f$ …
2answers
754 views

### Numerical Computation of arcsin and arctan for real numbers [closed]

I'm coding some numerical methods and I do not know what the correct analysis would be for choosing the implementation for $arcsin$ and $arctan$ for real numbers. Here's what I kno …
1answer
127 views

### nonlinear delay differential equation

Consider the delay differential equation: $y_x(x) = \sqrt{y(x-\bar{x})}$ where $y$ is the unknown function of $x$, and where $\bar{x}$ is a fixed parameter. This equation doe …
2answers
914 views

### Integral representation of higher order derivatives

I'm quite curious about the following phenomena, that still puzzle me although I have a proof, and I'd be really glad if someone may shred some light, showing an interpretation or …
3answers
2k views

### Is there an “elegant” non-recursive formula for these coefficients? Also, how can one get proofs of these patterns?

Hi. Not sure if this is a "good" question for this forum or if it'll get panned, but here goes anyway... Consider this problem. I've been trying to find a formula to expand the " …
5answers
2k views

### Roots of truncations of e^x - 1

During a talk I was at today, the speaker mentioned that if you truncate the Taylor series for $e^x - 1$, you'll get lots of roots with nonzero real part, even though the full Tayl …
1answer
325 views

### Approximation:- Algorithmic considerations

Hello I want to approximate a function $f$ on $(a,b)$. The function is singular at the points $a$ and $b$, however I have asymptotic expansions at these points. I can also constr …

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