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    Showing Integral form satisfies the Airy function

    surely the positive and negative components of the cos function will add up to zero when you integrate ?
  2. T

    Showing Integral form satisfies the Airy function

    Hey All, Can someone please give me the gist of how to show that the integral form of the Airy function for real inputs: Ai(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\tfrac13t^3 + xt\right)\, dt, satisfies the Airy Differential Equation: y'' - xy = 0 I tried differentiating twice...
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    Method of residues integration problem

    Hi all, I am trying to determine two Melnikov Integrals (after some manipulation) of the form: \int^{\infty}_{-\infty}cos(at)sech(bt) dt and \int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar...
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