Bessel functions Jn are missing from SMath Studio.

"J" index "n" is a set of Bessel functions which we should enter J[n(x) or J(n,x) in SMath sheets.
Bessel functions are defined for nay index n which is a positive real number or a negative integer.

Any Bessel function defined with a classical series is very slowly computed or does not give an accurate result.

Bessel functions Jn are missing from SMath Studio.

"J" index "n" is a set of Bessel functions which we should enter J[n(x) or J(n,x) in SMath sheets.
Bessel functions are defined for nay index n which is a positive real number or a negative integer.

Any Bessel function defined with a classical series is very slowly computed or does not give an accurate result.

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That wish list came few weeks ago, and I have few points in there:
1. Guiseppe Borzi made lot of advanced functions available for Mathcad 8 but I have no recollection if it is
because they were not included in Mathcad 8. In Mathcad 11, all Bessel exist but naturally they are not
accessible. It they would be, just plug them in Smath "UserEFI".
2. That said, all if not all numerical math functions are computed in Padé "Normalised Rational functions"
for their numerical stability and speed of execution and "Automata prallel machines". Also, recursive Tchebyshev
may be used [accurate, but slow ... 3 times the computing load vs Padé, no prallel computation]

Some sources:

Abramowitz & Stegun, Clenshaw small booklet for Chebyshev,
Padé rationalfractions are collected in "Hart et al."
In "Cody junior" you will see how much it takes to implement in a PC.
Tthe other one I have is "Luke". It gives lot of them complete in Fortran.

More interesting and most important:

Maxima X_Y plot is a piece of crap to me except for for what it can do
Nice is the grid setting and label digit format, some symbols ...
But it is the only gear in my 15 years maths that plots f(x,y) contours
even Mathematica does not from reading their recent "StackExchange" forum.
In Mathcad we can from Tom special program.

The Smath quick plot can't set the label format, very anoying in most plots
and it plots what it wants to plot ... Ah ! It does plot some Sigma series
[my XFR function ... ] but it refuses my Lagrange. In all my works of fitting
data set [several 100's, I have converted all my Padé rational in J-Fractions
via the Maple that comes with Mathcad 11. J-Fractions are continued fractions
from old Fortran that minimises the the number of Aops [Arithmetic operations]
Smath loves J-Fractions and it spits the nth derivatives perfect.

About plotting: dot, dashdot ... there is no chiken dining with pieces of traces
it's done by dropping part of the plotted data. "dot" is no problem and I have it
by simple decimation of the data [little program in Smath]. For dashdot, the matter
is to decimate in sequence [I don't have it done in program, feasible]. "dash" is
another version of "Dashdot" ... both are RemToDo.

I wouldn't take Scientific governance for uniquely "black plot", that is decades
retardation ... just figure Smith chart all in black ... BS ! Only some men are
partially color blind, ladies are not color blind.

Back to bessel: in the old Mathematica, they gave all the expansions as implemented
in the working version [Mathematica 4.0]. Whether it will work in Smath ???

You may have missed one point about Smath, before going too far:
You can't write J(n,x):= (,,,) where 'n' is an index, Smath does not take an index
in the LHS. I have done it otherwsise by using the Smath undocumented local definition
in the RHS. It works fine for my De Boor spline and in other works.
For your Jn Bessel, you may force maple( ,,) to compute particular points but that is
to be verified because Smath cracks Maple engine only up to line 21 and if that Bessel
is longer than 21 lines of code, zap: error message

Few days ago, some collab wanted "LambertW", I just plugged it in "Samples"
No back news, no comment. This LambertW, I will repost it today with lot more examples
that highlight many limits in Smath vs Mathcad 11.

jmG

Try this: Cephes Math Library

Hi Jean

I agree with you about the plotting capabilities of SMath incl. plugins (except, of course the Maxima-plugin, using gnuplot for plotting, by Martin and Kay, which unfortunately is not available for Linux users).

Some time ago I proposed Veusz (programmed by Jeremy Sanders under GNU-licence http://home.gna.org/veusz/) as a possible candidate for a plotting plugin.

See my post: http://smath.info/forum/yaf_postst2523_Possible-candidate-for-new-plotting-plugin.aspx

Tinu

Hello Tinu,

I would also like the Veusz inside SMath and I suppose many other (users) as well, but there is not a problem what we (users) would like - the problem is WHO could or would implement it into SMath.
Unfortunately, there are still only few good willing people (developers) here and it depends on their preferences, spare time etc. We may give them our wishes but it is up to them what they choose to develop or improve inside SMath. All my respect to the SMath developers

Regards,
Radovan

Hello: Tinu, Radovan

It's just because we don't know how to create GNUplot in Smath.
As it looks, it seems we should be working backwards
1. Create a project file of similar code than GNU model
But can we just invent one or take the next logical sequence ?
I figure the GNU Smath model or the one you create is a public link
to GNU. If it would be so, unfortunately the plots would not be
resident in Smath to the contrary of Mathcad.
2. The other step is the creation of the 3D itself with all specifics.

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Back to Bessel functions

As you know they are independent solution of the Bessel DE.
For a complete Bessel system, you need the two first of each kind
the suite is by recurrence.

So you need: Jzero, Jone .... Yzero, Yone.

I have the 4 of them in hand [Hart et al.], 25 decimals, range 0..8
It's about 2 hours work [no problem] ,,, but I wouldn't be able
to sanity check vs Mathcad [only some cross check].

They are on my ListToDo.

In few minutes, visit "Samples" for the very useful simple Gaussian spline.
There are few more to come, if "codable".

Jean