| Looking for Mittag-Leffler function [message #37991] |
Wed, 11 February 2004 08:28  |
mzkiss
Messages: 2
Registered: February 2004
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Junior Member |
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Hi everyone! I am trying to write a code which will generate the
Mittag-Leffler function,
E_alpha(x) = sum(k = 0 to infinity) (x^k)/gamma(alpha*k + 1).
There are more general cases, but in this particular application,
x is real, and alpha is between 0 and 1. Oh, and as a special case,
if alpha = 1, then this reduces to exp(x). My problem is that coding
it up as is works up to a point before reaching machine limits (x^k
for large x and large k, as well as large values of the gamma
function), but I need solutions for large x (x >= 20).
Can anyone point me in the right direction?
Thanks,
Mik Kiss
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| Re: Looking for Mittag-Leffler function [message #38065 is a reply to message #37991] |
Fri, 13 February 2004 11:44  |
mzkiss
Messages: 2
Registered: February 2004
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Junior Member |
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Sure! The subject is viscoelasticity of solids. In one particular
viscoelastic model, the stress is a function of the strain and strain
rate. Well, a modified version of this model replaces the strain rate
with a fractional derivative (with the fraction between 0 and 1). So,
if the solid is subjected to an impulse stress, according to the
model, the creep compliance solution is a Mittag-Leffler function.
This is a bit glossed over, but it's the guts of the problem.
Mik Kiss
meinel@aero.org (Ed Meinel) wrote in message news:<63342373.0402130651.4206d1b8@posting.google.com>...
>> mzkiss@wisc.edu (Miklos Kiss) writes:
>>> Hi everyone! I am trying to write a code which will generate the
>>> Mittag-Leffler function,
>>>
>
> Wow, I haven't heard anyone say "Mittag-Leffler" since my days in
> graduate school! Could you tell us what you are using them for?
>
> Ed Meinel
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