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I am wondering if I can be so lucky that any of you would know, if these two functions -- defined by the bellow integrals -- have a "name"/are well known. I have sporadically sought through the entire Abramowitz and Stegun without any luck.

[itex]f(x,a) = \int_0^\infty\frac{t\cdot J_0(at)}{t^2 + x^2}\,\mathrm{d}t [/itex]

and

[itex]g(x,a) = \int_0^\infty\frac{t^2\cdot J_0(at)}{t^2 + x^2}\,\mathrm{d}t [/itex]

where [itex]J_0(x)[/itex] is the Bessel function of the first kind.