Hi,
as a newbie I want to check some relations between Bessel functions
and Zernike polynomials.
To get some ideas first I tried to plot Bessel functions of different
type as indicated in the Bessel?.
To be able to distinguish the different types one wants to use color,
but something like
g = Bessel(2); g.plot(1,11,color='red')
does not work. Obviously, I did not realize that this plot is a
special plot function.
To find out I tried
type(g)
and got 'instance' which did not help me very much.
g.parent()
is not valid and Bessel?? gives the source code starting at line 942
but terminating (!) with a
Traceback (click to the left of the block for traceback)
I needed to consult sage-support to see how to plot Bessel functions
with individual colors.
Now, in order to establish some relations to Zernike polynomials I
need to integrate.
Naive aproaches like
vars=var('x');integrate(Bessel(2)(x),x,1,2)
which results in 'Cannot evaluate symbolic expression to a numeric
value',
or the 'lambda trick' as somebody on sage-support called it
integrate(lambda x: Bessel(2)(x),x,1,2)
which results in a laconic 'Type error' did not give me a clue.
Because I am not sure about the type/class of the object Bessel
(see above) I do not know what else try (I hate trial and error).
Of course I can take to numerical_integral
but if Bessel functions are implemented in a proper class
then maybe there is another way I did not spot.
Any hint about how to proceed properly
and how to integrate symbolically
is very much appreciated. Thomas
PS is the special Bessel plot function a good idea,
if dummies like me are lured into expecting too much?
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