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Re: Numerical calculation of a double sum (Appell's function F4)

• To: mathgroup at smc.vnet.net
• Subject: [mg75352] Re: Numerical calculation of a double sum (Appell's function F4)
• From: dh <dh at metrohm.ch>
• Date: Thu, 26 Apr 2007 03:31:41 -0400 (EDT)
• References: <f0n8j5$s6s$1@smc.vnet.net>

Hi Markus,

Are you aware that Sum can do double sums?

Daniel



Markus Huber wrote:

> Hello,

> 

> I am working currently with double hypergeometric sums. Unfortunately

> the one I need (Appell's F4) is not implemented in M. So I decided to

> write my own F4.

> I discovered quickly that this a far more complicated task than

> expected, which is due to many special cases of the arguments (e.g.

> the series can be truncated, transform into another series or have

> singularities in Gamma functions; there are also cases where these

> singularities cancel). I managed to overcome all those difficulties,

> but still I wonder, if there is an easier solution to the following:

> 

> F4 is a double sum. My approach is a simple While loop (ok, it's more

> complicated, because cancelling singularities can lead to intermediate

> terms that are zero and so you have t think carefully about getting a

> quantity that tells you when the desired accuracy is reached). Is

> there a function in M that can do double sums numerically and also

> checks for convergence?

> 

> I appreciate any help, because this - I would guess - would make the

> calculation faster and the code more readable.

> 

> Thanks for any suggestions

> 

> 

> Markus Huber

> 

> 

> PS: Don't be misled by the seeming simplicity of Appell's Function F4

> when you look it up. In all probability you will only find the

> standard series representation. There are also other representations

> with other regions of convergence that exist of 5 single

> hypergeometric series. Esp. those I need.

> 

>