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Results tagged with ca.classical-analysis-and-odes
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user 53092
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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How to find an annihilating linear ode for a class of integrals depending on a parameter?
Given two polynomials $a(t)$ and $b(t)$, consider the integral
$$C(z)=\int_0^1 \frac{dt}{\sqrt{(z-b(t))^2+a(t)}}.$$
For $z$ near $\infty$, $C(z)$ is a well-defined analytic function which can be e …
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