ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 07 Jun 2017 20:55:07 -0500integral containing products of bessel functionshttp://ask.sagemath.org/question/37836/integral-containing-products-of-bessel-functions/I am trying to find a closed form expression of an integral containing a product of bessel functions. Sage returns my command instead of a solution. Any help is appreciated. My code is below. I am solving this on a free CoCalc server.
phi, l, R, r_bar= var('phi l R r_bar')
phi = bessel_J(0, l*R) - (bessel_J(0,l*r_bar)*bessel_Y(0,l*R))/(bessel_Y(0,l*r_bar))
f = R*phi*phi
integrate(f, R)RieszRepresentWed, 07 Jun 2017 20:55:07 -0500http://ask.sagemath.org/question/37836/Arbitrary precision BesselYhttp://ask.sagemath.org/question/9679/arbitrary-precision-bessely/Hi,
I consider using Sage for some calculations which contain Bessel functions of complex arguments. Since I have to mix Bessel functions with very small and very large arguments I require precision higher than 15 digits.
Unfortunately, I recognized that BesselY is not implemented in PARI. But BesselJ and BesselH1 are. My physicists understanding of math tells me, I could just use "(BesselH1-BesselJ)/i". But I am surprised that this has not been discussed before (at least I couldn't find it), since this would allow a quick implementation of BesselY. Am I missing something that's obvious for math experts? Or can I just use above definition to get an arbitrary precision BesselY?
Many thanks
Frank
FrankStThu, 03 Jan 2013 02:52:57 -0600http://ask.sagemath.org/question/9679/summing over bessel functionhttp://ask.sagemath.org/question/8148/summing-over-bessel-function/Hi.
I need to sum over a bessel function K:
sum(bessel_K(0,2*PI*abs(x+k)),k,-oo,oo)
How ever I get an error:
>TypeError: Cannot evaluate symbolic expression to a numeric value.
Which sounds logical. I there any way around this?
Thanksyotama9Sun, 05 Jun 2011 05:26:22 -0500http://ask.sagemath.org/question/8148/Symbolic expressions and simplifyinghttp://ask.sagemath.org/question/7852/symbolic-expressions-and-simplifying/I asked this on IRC, but no-one seemed to be on there.
I had a quick question concerning simplifying a symbolic expression in sage.
Basically, when i do a Laplace transform, i end up with the RHS of the following equation, but I would like to see the LHS of the equation
http://upload.wikimedia.org/math/a/1/7/a1752ef3bbff0288217159ca274c5bc8.png
Would anyone know how to change from one side to the other side please?
CoolHanDrewSat, 08 Jan 2011 00:22:02 -0600http://ask.sagemath.org/question/7852/Bessel functionshttp://ask.sagemath.org/question/7878/bessel-functions/A couple of questions about Bessel functions:
(1) Shouldn't this return return a symbolic expression, so that it can be used as part of an expression to be evaluated later with a specific r:<pre>
sage: var('r')
sage: bessel_J(0,r)
</pre>
I'm thinking specifically of building up a series that will later be plotted.
(2) There was talk a while back about making the zeros of the Bessel functions available without having to calculate them with find_root() (Not that there's a problem doing that, but it would just be a convenience.) I was just wondering if anything came of that.
Mike WittSun, 16 Jan 2011 09:44:24 -0600http://ask.sagemath.org/question/7878/