A linear equation is $$ ax + b = 0 ; \,\, \,\, a\neq 0 $$ A quadratic equation is $$ax^2 + bx + c = 0 ; \,\, a\neq 0 $$ And so on... Why are all these equ...

The question is : Determine all functions f satisfying the functional relation $f(x)+f\left(\frac{1}{1-x}\right)=\frac{2(1-2x)}{x(1-x)}$ where $x$ is a re...

I recently ran into the following exercise: Evaluate $$\oint_\Gamma\frac{\cos z}{(z-\pi)^2}dz,$$where $\Gamma$ is a complete circuit of the circle $|z|=1$...

I am looking for an example where you have $P(n)$ implying $P(n+1)$. However there is no base case. For which there is therefore no solution at all for th...

I'm trying to prove that ${n \choose r}$ is equal to ${{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$. I suppose I could use the counti...

I found this definition of total variation of a function $F(x, y)$ \begin{eqnarray} dF(x, y) &\equiv& F(x+dx, y+dy) -F(x, y)\\ & = & [F(x+...

I am confused by the Taylor's Inequality formula: $$|R_n(x)| \le \frac M{(n+1)!}|x−a|^{n+1}$$ What do $R_n$, $M$, $n$, $x$, $a$, stand for i.e. what ...

I am currently in Geometry, doing proof, when me, my teacher, and my classmates realized that the exterior angles of a polygon are equal to the central an...

Disclaimer: I'm an engineer, not a mathematician Somebody claimed that $\gcd$ only is applicable for integers, but it seems I'm perfectly able t...

So, as far as I have learned, a complex function $f(u)$ is considered harmonic if and only if it satisfies the undermentioned equation: $$ \frac{\partial ...