I'm not sure of the Maple function I have to use to represent the modified Bessel function of the third kind with index 1.

The Bessel function of the third kind is also named the Hankel function.

I mistakenly started to use HankelH1 or HankelH2 but quickly realized they are both complex-valued functions while the paper I'm working on uses a real-valued modified Bessel function of the third kind: finally, does this latter exist in Maple 2015?

Thanks in advance

I feel that it is increasingly common for answers to generate no reaction from their authors.

Perhaps the author simply voted up... but in that case, would it be possible to indicate this (something like "XXX voted up")? 

This would avoid wasting time responding to the same author in the future, as it doesn't seem to care about commenting the answer.

I'm struggling to construct a statistical Distribution involving Product.
This is likely a question of delayed evaluation but I'm not capable to fix it.
Can you please look to this  Product_error.mw  worksheet  and help me fixing the issue?

Thanks in advance

A classical probability result says that if G₁ and G₂ are two independent Gamma random variables with same scale parameter (let's say 1 to simplify) and shape parameters a₁ and a₂ respectively, then G_k / (G₁ + G₂ ) is a Beta random variable with parameters (a_k , a_3-k ) (k=1..2).

In the attached file it is shown that (Maple 2015) function Statistics:-PDF fails in computing the PDF of G_k.
Noting strange here if you observe that even in the extremely simple case Z = X / (X+Y), where both X and Y are independent Uniform random variable with support [0, 1), Maple 2015 already fails in computing PDF(Z).

An alternative to Statistics:-PDF is to write explicitely the double integration which defines CDF(Z) (to begin with, and later PDF(G_k)) and ask Maple to do the integrations.
This approach works for Z but requires helping Maple when X and Y are still independent Uniform random variables but with respective non instanciated supports [0, a₁) and [0, a₂).

Applying to the Gamma-Gamma case the recipies I introduced in the Uniform-Uniform case does not give any result, unless in the very particular case where the shape parameters a₁ and a₂ are (strictly) positive integers.

All the details are in X_over_(X_plus_Y).mw

Do you have any idea how to prove with Maple the probability result mentioned at the head of this question?

PS: The "classical method" to do compute PDF(Z) consists in changing the integration variables < x₁, x₂ > into < x₁ = v₁v₂, x₂ = v₂ (1-v₁) > (see for instance Stack exchange)... but even after having dome it I still cannot get the desired result.

Thanks in advance.

For years I used to use 2 accounts when I am home

• one under Firefox corresponds to my profesionnal account, which I can access to from my office oror home (and which is the one I use here),
• the other one under Safari is my "personal" account; (login mmcdara)  which I cannot access to from my office because of security rules.
   

To separate the managing of professional and personal accounts I always used the former under Firefox and the latter under Safari.
Since the outage my personal account is no longer accessible, neither from Safari nor Firefox.

I created this account about eight years ago using the adress michael.mcdara@gmail.com and during all these years the connexion to Mapleprimes from Safari was  "automatic" in the sense that I was always logged in as mmcdara. Even after having quit Safari or shut down my computer, I was logged in as mmcdara as soon as I reopened Mapleprimes (a curiosity, for quitting Firefox being logged in as sand15 and openening it again required my relogging as sand15).

This still was the case early this morning (I sent replied to andiguy) but not one hour after.
Indeed Mapleprimes asked me my mail adress, that I knew, and my password, that I have forgot, of course.

Eight years ago the double authentification was not mandatory and so Gmail has purely and simply made the adress michael.mcdara@gmail.com inaccesible in between (I used it only with Mapleprimes, thus no real need to look at it regularly nor to bother with this double authentification stuff... at least I thought).
So any attempt to ask for a reinitialization of my password is a dead end for I cannot access the address michael.mcdara@gmail.com

My main activity on Mapleprimes is realized using my mmcdara account.
What bothers me the most  (loosing my mmcdara account would be unplesant but I can survive this) is that I was working since several months on two or three posts and that I can't anymore access the corresponding drafts (not a deadly situation I cannot survive to neither).

Do you have any idea about how to solve these issues?
I would satisfy myself recovering the two or three post drafts I was working on.

Thanks in advance