query: $(x-x_0)^0$ in power series
positive_passages.docid: 14150
positive_passages.text: Zero to the zero power – is $0^0=1$?
negative_passages.docid: 143756
negative_passages.text: Introduction to Analysis: Multiplication Theorem for Series
negative_passages.docid: 61361
negative_passages.text: Find the set of $x>0$ such that the series $\sum\limits_n x^{\ln{n}}$ converges
negative_passages.docid: 36799
negative_passages.text: Maclaurin series for $\frac{x}{e^x-1}$
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 43320
negative_passages.text: Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$
negative_passages.docid: 142288
negative_passages.text: How to solve the diffencial equation for power series $(1+x²)y'' - 6xy=0$ in $x_{0}=0$
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 140437
negative_passages.text: If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$
negative_passages.docid: 150600
negative_passages.text: Radius of Convergence of a given Power series
negative_passages.docid: 137997
negative_passages.text: Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $x\in [0,1)$?
negative_passages.docid: 140221
negative_passages.text: Product of two power series
negative_passages.docid: 6416
negative_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 42189
negative_passages.text: Ring of rational-coefficient power series defining entire functions
negative_passages.docid: 39302
negative_passages.text: Radius of convergence of a sum of power series
negative_passages.docid: 42736
negative_passages.text: Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
negative_passages.docid: 25370
negative_passages.text: Power series of a function