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Re: [Maxima-discuss] bessel, integration, was Re: bfloat
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From: Barton W. <wi...@un...> - 2018-11-13 18:23:33
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For big float evaluation of Bessel's J function, you could use DLMF 10.16.9 (https://dlmf.nist.gov/10.16#info) along with Maxima's hypergeometric function. That might be slow, but it does do big float evaluation. Let us know if that works --Barton ________________________________ From: Richard Fateman <fa...@be...> Sent: Tuesday, November 13, 2018 11:46:58 AM To: max...@li...; ma...@et... Subject: [Maxima-discuss] bessel, integration, was Re: bfloat First, there is a bigfloat version of romberg numerical intergration, but it seems to have lost any documentation. load (brmbrg) then bromberg(x^2,x,0,3); works. So there is a bug in documentation, and autoloading. Next, of course the function that you are integrating must be able to compute with bigfloats, and apparently the bessel_j program in Maxima right now doesn't do that. If you are seriously interested in high-accuracy bessel functions, there's a ton of material, and software. Small and asymptotic versions. Depending on the range and the order, there are taylor series as well. However your question is kind of vague, suggesting either you are just diddling around (which is OK, but you could say so, and -- for example -- offer to implement better software...) or you have an objective in mind that (you think) requires bessel_j numerical integration, but you might be wrong, and if you told us the objective it might suggest another approach entirely. (Like Taylor series.) Why do you think bfloat integration is necessary? Did you try the existing float integration routines and find they had some problem, like inadequate error estimates? overflow? You could tell us about that, too. And what kind of error estimate or bound do you think you need (and perhaps why...) RJF On 11/13/2018 7:51 AM, Stavros Macrakis (Σταῦρος Μακράκης) wrote: bessel_j(1,2.3b0) returns a noun form, which indicates that bessel_j doesn't work with bfloat arguments. It should be more explicit in the documentation that it calculates a numerical result for float arguments but not bfloat. On Tue, Nov 13, 2018 at 2:29 AM Ether Jones <ma...@et...<mailto:ma...@et...>> wrote: I want to use arbitrary precision (bfloat) floating point to numerically integrate a function which calls bessel_j() function. Does Maxima support this? If so, could you please post a very simple example showing the proper syntax to assure that fpprec is used for all intermediate calculations? Thank you. _______________________________________________ Maxima-discuss mailing list Max...@li...<mailto:Max...@li...> https://lists.sourceforge.net/lists/listinfo/maxima-discuss<https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.sourceforge.net_lists_listinfo_maxima-2Ddiscuss&d=DwMDaQ&c=Cu5g146wZdoqVuKpTNsYHeFX_rg6kWhlkLF8Eft-wwo&r=Ln0CjFotuA7GyhsRS-QpQA&m=kYtQjrBUz7X9knf_dSQnPQO_9k8Sbttx6G6ozIuEA7o&s=IwWUDJ4kJoizDMepR-2WbIfPDoIArZ0y4IMCmJ_JtUY&e=> _______________________________________________ Maxima-discuss mailing list Max...@li...<mailto:Max...@li...> https://lists.sourceforge.net/lists/listinfo/maxima-discuss<https://urldefense.proofpoint.com/v2/url?u=https-3A__lists.sourceforge.net_lists_listinfo_maxima-2Ddiscuss&d=DwMDaQ&c=Cu5g146wZdoqVuKpTNsYHeFX_rg6kWhlkLF8Eft-wwo&r=Ln0CjFotuA7GyhsRS-QpQA&m=kYtQjrBUz7X9knf_dSQnPQO_9k8Sbttx6G6ozIuEA7o&s=IwWUDJ4kJoizDMepR-2WbIfPDoIArZ0y4IMCmJ_JtUY&e=> |
