query: Find $a_1/a_2$ in the Laurent series expansion of $\frac{1}{2z^2-13z+15}$
positive_passages.docid: 142445
positive_passages.text: Laurent series expansion of a given function
negative_passages.docid: 119628
negative_passages.text: Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
negative_passages.docid: 121128
negative_passages.text: Calculating a Residue at one of the poles of $\frac{1}{1+z^n}$
negative_passages.docid: 21121
negative_passages.text: Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
negative_passages.docid: 10141
negative_passages.text: Find closed form expression for series expansion coefficients
negative_passages.docid: 121554
negative_passages.text: Finding $\sum\frac{1}{2^n(n+1)}$
negative_passages.docid: 60456
negative_passages.text: Find the power series of $f(x)=\frac{1}{x^2+x+1}$
negative_passages.docid: 65645
negative_passages.text: Express $w$ and $\frac1w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
negative_passages.docid: 76532
negative_passages.text: Two different expansions of $\frac{z}{1-z}$
negative_passages.docid: 131276
negative_passages.text: Maclaurin series of $\ln(1-x+x^2)$
negative_passages.docid: 34059
negative_passages.text: $(a^{2^n}+1,a^{2^m}+1)=1 or 2$
negative_passages.docid: 126791
negative_passages.text: If $2a_{n+2} \le a_{n+1}+a_n$, then $\lim \sup a_n \le \frac23 a_2 + \frac13 a_1$
negative_passages.docid: 75423
negative_passages.text: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
negative_passages.docid: 4015
negative_passages.text: Maclaurin Expansion for $e^{e^{z}}$ at $z=0$
negative_passages.docid: 129236
negative_passages.text: Continued fraction for $\frac{1}{e-2}$
negative_passages.docid: 31856
negative_passages.text: Find $a^{2013} + b^{2013} + c^{2013}$
negative_passages.docid: 12812
negative_passages.text: Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $