Intereting Posts

The average of the roots of a polynomial equals the average of the roots of its derivative
How can I pick a random point on the surface of a sphere with equal distribution?
Software for generating Cayley graphs of $\mathbb Z_n$?
Expression for $\int_0^1 x^n(1-x)^{n}/(1+x^2) \ dx$
A structural proof that $ax=xa$ forms a monoid
Geometrical interpretation of $I(X_1\cap X_2)\neq I(X_1)+I(X_2)$, $X_i$ algebraic sets in $\mathbb{A}^n$
a question about Fourier transforms
The myth of no prime formula?
Trouble with gradient intuition
How prove this $(abc)^4+abc(a^3c^2+b^3a^2+c^3b^2)\le 4$
After $t$ hours, the hour hand was where the minute hand had been, and vice versa
Why should I care about adjoint functors
Expected Value of a Determinant
Existence of a dense proper subset with non-empty interior?
What are the units of cyclotomic integers?

I have been playing around with infinite series and I wondered if it is possible to find an expression for the series:

$$

\sum_{k=0}^\infty x^{p(k)}

$$

as a generalization of geometric series. $p(k)$ is an arbitrary polynomial.

- Irreducibility of Polynomials in $k$
- Fact about polynomials
- $P(x)\in\mathbb Z$ iff $Q(x)\in\mathbb Z$
- Polynomials, finite fields and cardinality/dimension considerations
- Is $\frac{x^2+x}{x+1}$ a polynomial?
- The number of real roots of $1+x/1!+x^2/2!+x^3/3! + \cdots + x^6/6! =0$
- What is a Resolvent?
- When can Galois theory actually help you find the roots of a polynomial?
- Prove the following (algebra of polynomials)
- Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$

- Distinguishing Primitive vs. Nonprimitive Roots of Unity
- Why is $\cos(x)^2$ written as $\cos^2(x)$?
- If nonempty, nonsingleton $Y$ is a proper convex subset of a simply ordered set $X$, then $Y$ is ray or interval?
- Help understand canonical isomorphism in localization (tensor products)
- $q$-norm $\leq$ $p$-norm
- A holomorphic function is conformal
- Repeated Factorials and Repeated Square Rooting
- Eigenvalue of a linear transformation substituting $t+1$ for $t$ in polynomials.
- What concept does an open set axiomatise?
- If Ax = Bx for all $x \in C^{n}$, then A = B.
- How to prove continuity of $e^x$.
- Show that $SL(n, \mathbb{R})$ is a $(n^2 -1)$ smooth submanifold of $M(n,\mathbb{R})$
- Outer measure is countably subadditive
- Show that ideal is a subring
- Number of Trees with n Nodes