[Scilab-users] Si function => expint()

[Samuel Gougeon]

Le 07/02/2020 à 00:02, Samuel Gougeon a écrit :
> Le 06/02/2020 à 10:41, Federico Miyara a écrit :
>>
>> Dear All,
>>
>> Just in case somebody is interested, find attached a Scilab function 
>> to compute the sine integral function Si (the integral from 0 to x of 
>> the sinc function), which cannot be expressed in closed form with 
>> elementary functions.
>>
>> /It is preliminary, it doesn't test for appropriate input argument.
>>
>> It works for real or complex matrices or N-D arrays.
>>
>> It can be easily modified to get the cosine integral function.
>> /
>
> Great work, Federico! Just a comment: IMHO, so short functions names 
> should really be avoided.
> The shorter the name, the more probable are collisions with other 
> users common variables.
>
> By the way, i am wondering about a similar expint() function = 
> integral of dt*exp(t)/t.
>
> From there, the linearity of the integration operator and the Euler 
> formula would yield
> in a trivial way sinint(a) and cosint(a), with a (almost) one-line 
> definition using
> expint([-a a]*%i).
>
Of course, the same expint could then be used as well for 
integral(dt.sh(t)/t),
integral(dt.ch(t)/t), etc. The exp familly is great, and, IMHO, there 
would be
no need to create N specific functionint for trivial expint combinations.
Just a good set of expint applications examples, in the expint 
documentation.

Samuel

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