# Tagged Questions

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226 views

### A question on partial fraction decompositions

This question concerns a mapping from the poles of a rational function to its partial fraction decomposition coefficients. We assume that the rational function is the inverse of a polynomial of degree ...

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32 views

### Truncation error in Padè approximants

Suppose only the following data are known about a rational function $R(x)=P(x)/Q(x)$ (for $P,Q$ polynomials):
(a) the degree of $P$ is $\leq m$ and the degree of $Q$ is $\leq n$;
(b) the first $k$ ...

**2**

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**2**answers

158 views

### Finding a simpler “local” lower bound for a rational function

I have obtained as the expression for some quantity the following gargantuan formula:
$$ \frac{k^8 + 3k^7 + 8k^6 + 3k^5 - 16k^4 - 32k^3 + 63k^2 - 34k + 6}{k^6 + 3k^5 + 6k^4 - 24k^2 + 21k - 5}$$.
...

**8**

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**1**answer

321 views

### certain trigonometric homeomorphisms

Are there any simple characterizations of rational functions $f(x,y)$ with real coefficients such that $\theta\mapsto f(\cos\theta,\sin\theta)$ is a homeomorphism from $\mathbb R\bmod 2\pi$ to ...

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338 views

### Properties of a rational function of multiple variables

Suppose you are given a multivariable rational function f(x0,x1,x2,x3,..,xn), so the only four operation are +,-,*,/.
Assume that all constants and exponents are integers within certain range.
I ...

**0**

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**0**answers

296 views

### Absolute minima for rational function

Suppose I have two rational polynomials $f_1 (x)$ and $f_2 (x)$, both of the form
$$
f_k (x) = \frac{x (A_k x + B_k)}{(C_k x + D_k)}
$$
with constants $A_k, B_k, C_k$ and $D_k$ and where $k=1,2$. I am ...

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**3**answers

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### Rational exponential expressions

Consider the following extension of polynomials. The rational exponential expressions (REXes) are given by:
The leaves 1 and $x$ for $x$ drawn from a class of variables; and
Closed under the binary ...