hankel_transform definition

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jak137
2011-10-06
2012-11-20
  • jak137
    jak137
    2011-10-06

    Hi,

    I am puzzled by the definition of hankel_transform. Usually it is defined as:

      f_\nu(k) = \int_0^\infty F(r) J_\nu(kr) r dr

    while in defint the definition is:

      f(\omega) = \int_{0}^\infty F(t) J_\nu(2 \sqrt{\omega t}) dt

    (note the lack of r term and square root of the product).
    What is the source of this definition and how can one compute the "normal" Hankel transform?

    Also: Is it possible to compute integrals with spherical Bessel functions with reduce?

    Thanks in advance for any help,
    Jaroslaw