query: three term asymptotic solution as $\epsilon \to 0$
positive_passages.docid: 29250
positive_passages.text: obtain a three-term asymptotic solution
negative_passages.docid: 144841
negative_passages.text: Find general solution $y''y^3=1$
negative_passages.docid: 97720
negative_passages.text: Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
negative_passages.docid: 56206
negative_passages.text: Symmetry of the $3\times 3$ Cauchy Stress Tensor
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 153727
negative_passages.text: Constant term in Lagrangian
negative_passages.docid: 19729
negative_passages.text: An infinite dimensional limit
negative_passages.docid: 104269
negative_passages.text: Why does $\lim\limits_{t\to-\infty}te^t=0$?
negative_passages.docid: 4015
negative_passages.text: Maclaurin Expansion for $e^{e^{z}}$ at $z=0$
negative_passages.docid: 14517
negative_passages.text: Existence of solutions of the equation with a limit.
negative_passages.docid: 41419
negative_passages.text: Solution of limit $\lim\limits_{x\to 0} \frac {e^{-1/x^2}}{x} $
negative_passages.docid: 74692
negative_passages.text: Simple Power Series Expansion for Problems similar to $f = (1 + \epsilon \,x)^{1/\epsilon}$
negative_passages.docid: 101112
negative_passages.text: Transport equation $u_t + xu_x + u = 0$ with $u(x_0, 0) = \cos(x_0)$
negative_passages.docid: 101213
negative_passages.text: General distributional solution of the Airy Equation
negative_passages.docid: 67350
negative_passages.text: Analytic solution of: ${u}''+\frac{1}{x}{u}'=-\delta e^{u}$
negative_passages.docid: 153238
negative_passages.text: Simple question on perturbation theory for a function with two small parameters
negative_passages.docid: 36648
negative_passages.text: The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$