# [✓] Calculate Bessel Function zeros? (Can PayPal for solution)

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 Michael M 1 Vote I am working on a drum synthesizer based off the Bessel Function zeros. (The modal frequencies of a circular drum membrane are predicted by the Bessel Function zeros.)To built it, I have been manually calculating Bessel zeros using Casio's calculator: http://keisan.casio.com/exec/system/1180573472This is working. However, it is very slow work, as I am calculating each zero one by one, manually. Bessel equations in Wolfram are incredibly easy by contrast. How they work is summarized here: http://mathworld.wolfram.com/BesselFunctionZeros.html the Bessel function for nonnegative integer values of n and k can be found in the Wolfram Language using the command BesselJZero[n, k]. In an ideal world, I'd like bessel zeros to 6 significant digits for, n = 0...99 and k = 1...100. This would produce a table or list of 10,000 Bessel zeros.If it is easy, can anyone here maybe do me a huge favor and punch these into your Wolfram Language system to produce a table or list you can share? I would be happy to PayPal you $20 for your effort if so. If it's more work than that, let me know what it would cost.Otherwise, how would I set up my Windows system to do this? Can I work with Wolfram Language from Windows? I don't have a Raspberry Pi.I've calculated 1200 of these things manually which as you can imagine has been very tedious. While I'm getting the results I want, I will likely need at least 2000 more to get truly realistic results. I'd hate to spend days and weeks manually working out Wolfram can spit out in 5 minutes!In an ideal world, I'd like a table like this in Excel or any other workable format:Very hopeful for any help. Thank you very much.Mike Answer 10 months ago 4 Replies  J. M. 5 Votes Hello,Here's a nice pile of$J_n(z)$zeroes: https://pastebin.com/raw/vepKVF8sFor reference, here's the code that generated it: With[{count = 100, ord = 99, digits = 6}, Export["bz.dat", Table[NumberForm[N[BesselJZero[n, k]], digits], {k, count}, {n, 0, ord}], "Table", Alignment -> Left, "FieldSeparators" -> " ", TableHeadings -> {Range[count], Table[J[n, x], {n, 0, ord}]}]] Adjust the parameters in the first part of With[] for a bigger table or more digits. FWIW, you could try generating smaller-scale versions of the table from the free Wolfram Development Platform. Go here, and after it finishes loading, try With[{count = 50, ord = 20, digits = 8}, TableForm[Table[NumberForm[N[BesselJZero[n, k]], digits], {k, count}, {n, 0, ord}], TableAlignments -> {Left, Center}, TableHeadings -> {Range[count], Table[J[n, x], {n, 0, ord}]}]]  Answer 10 months ago  Michael M 1 Vote Thanks both of you guys but especially thanks J.M.!!! You are a lifesaver!!! That text file imports beautifully into Excel.Now I can play with it ...Can't believe how much time I wasted calculating the first 1200 by hand LOL. Well at least it proved the concept worked....Now I will see what it sounds like with 5-6x more many modes from all these other Bessel zeros...If you want the$20, PM or post your e-mail and I'll send it you by PayPal. Otherwise thanks for your good Samaritan deed. You've made my life a lot easier. Cheers.
 W. Craig Carter 3 Votes Here is a less robust method than J.M's but may be simpler to read.A list with 10000 rows and 3 columns: data = Flatten[ Table[ {n, k, N@BesselJZero[n, k]}, {n, 0, 99}, {k, 1, 100} ], 1 ]; Export that data to an Excel file in your Documents directory Export[FileNameJoin[{\$UserDocumentsDirectory, "Bessel_Zeros.xls"}], data] You can download the result here.