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Airy function - basic properties

I solve the Airy differential equation by Fourier transform and show that the Airy function satisfies the original DE by differentiating under the integral sign. This argument can be made rigorous by using complex analysis to consider a principal value integral

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L8.1 Airy functions as integrals in the complex plane

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a very Airy integral.

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The overpowered Laplace technique for summing series.

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The Airy Differential Equation

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Differential Equations | Series Solutions -- Airy's Equation

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Feynman's technique is the greatest integration method of all time

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Complex Analysis: Dogbone Contour Example

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Understanding Lagrange Multipliers Visually

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