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In particular:

[tex]

\Delta_+(x) = \frac{m}{4\pi^2\sqrt(x^2)} \int_{0}^{\infty}\frac{udu}{\sqrt(u^2 + 1)}sin(mu\sqrt(x^2))\hspace{2.5cm}(5.2.8)

[/tex]

or, in terms of a standard Hankel function,

[tex]

\Delta_+(x) = \frac{m}{4\pi^2\sqrt(x^2)} K_1(m\sqrt(x^2))\hspace{0.5cm}.\hspace{4cm}(5.2.9)

[/tex]

I can't find "Hankel" anywhere on PF, and wikipedia is no real help.

Surely integral (5.2.8) doesn't converge (the integrand oscillates between ±1)?

In fact, I think it's -∞.

So how can it be a standard function?

[size=-1]

*What am I missing?*[/size]