Newbetuts

$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

$\arctan$ of a square root as a rational multiple of $\pi$

Do holes affect the type of function (even, odd or neither)

If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.

If a rational function is real on the unit circle, what does that say about its roots and poles?

Families of curves over number fields

When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

Continuity of rational functions between affine algebraic sets

Convexity of a rational function

How to prove $\frac{1}{x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+2\sqrt{\frac{1}{ab}+\frac{1}{ac}+\frac{1}{bc}}$

Does there exist a nontrivial rational function which satisfies $f(f(f(f(x))))=x$?

Integration of rational of polynomials

Proof that rational functions are an ordered field, but non-archimedean - Bartle's elements of real analysis

Is there a general method to operate the reduction of a rational expression to a sum : $\frac {1+2x}{1-3x} \rightarrow 1+5x+\frac{15x^3}{1-3x}$

How to evaluate $\int 1/(1+x^{2n})\,dx$ for an arbitrary positive integer $n$?

Does $t^{p-1}$ have an antiderivative in $\Bbb F_q(t)$?

rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$

New posts in rational-functions

Finding good approximation for $x^{1/2.4}$

Embedding of a variety

Factoring when multiplying rational functions

$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

$\arctan$ of a square root as a rational multiple of $\pi$

Do holes affect the type of function (even, odd or neither)

If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.

If a rational function is real on the unit circle, what does that say about its roots and poles?

Families of curves over number fields

When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

Continuity of rational functions between affine algebraic sets

Convexity of a rational function

How to prove $\frac{1}{x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+2\sqrt{\frac{1}{ab}+\frac{1}{ac}+\frac{1}{bc}}$

Does there exist a nontrivial rational function which satisfies $f(f(f(f(x))))=x$?

Integration of rational of polynomials

Proof that rational functions are an ordered field, but non-archimedean - Bartle's elements of real analysis

Is there a general method to operate the reduction of a rational expression to a sum : $\frac {1+2x}{1-3x} \rightarrow 1+5x+\frac{15x^3}{1-3x}$

How to evaluate $\int 1/(1+x^{2n})\,dx$ for an arbitrary positive integer $n$?

Does $t^{p-1}$ have an antiderivative in $\Bbb F_q(t)$?

rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$