[Scilab-users] Si function

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[Scilab-users] Si function


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.

Regards,

Fderico Miyara

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Samuel GOUGEON Samuel GOUGEON
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Re: Si function

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).

Wouldn't they?

Best regards
Samuel


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Samuel GOUGEON Samuel GOUGEON
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Re: Si function => expint()

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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