Generalised Gamma Function

Adam Johansen
Wed Jan 15 14:05:00 GMT 2003

Many Thanks for your suggestions.

I apologies for not being clearer about what I was referring to -- and for
typing "distribution" whilst thinking "function" in the title.

> On Tue, 14 Jan 2003, Brian Gough wrote:
> > I'm not familiar with the definition, which function does it
> > correspond to in Abramowitz and Stegun?

I'm afraid that I don't thyink that there is a definition for it in
Abramowitz and Stegun. In actual fact it can be obtained trivially from
the Gamma function. The definition in Bernardo and Smith, "Bayesian
Theory", Wiley, 2002 p138 is:

Gamma_k(a) = Pi^(k(k-1)/4) * product(i = 1..k, Gamma(0.5 * (2a + 1 - i)))

Sorry if this is an unusual name for this function, or you know it as
something different.

I hope that's intelligible. This is, of course, a trivial product of
normal Gamma functions if the parameter a is restricted to real numbers.
I've implemented this, but I assume it's of no interest to anyone. My
application does, it transpires, only really require this case so I'm not
going to complicate things any further at this stage.

Brian: thanks for pointing out the gsl_sf_lngamma_complex_e function. I'm
not sure how I missed it, but this was, in fact pretty much exactly what I
was looking for.

Apologies for any confusion.


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