One small point about the Matern correlation function

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One small point about the Matern correlation function

Ruben Roa
Hi:
Maybe i am slightly offtopic (again). I would
like to point to the mathematical reasoning leading to
the Whittle-Matern correlation function implemented
by default in geoR. My doubt is in the passage from eq.
(62) to eq. (63) in Whittle's 1954 Biometrika paper, on
stationary processes in the plane. It is rather easy to
see the equivalence of these two equations but i believe
the random term on the rhs has changed its moments,
though Whittle may have thought trivial to say so. Anyone
cares to look at this and tell me if i am correct?
Cheers
Ruben