I can add two resources to the list: - N. W. McLachlan, Bessel Functions for Engineers - Chapter about Bessel Functions at NIST - http://dlmf.nist.gov/10
2015-01-26 17:28 GMT+03:00 grivet <[email protected]>: > Le 26/01/2015 10:57, Dang, Christophe a écrit : > > Hello, >> >> De Claus Futtrup >>> Envoyé : samedi 24 janvier 2015 17:53 >>> >>> I've made a small script to play around with Bessel functions of the >>> first kind >>> [...] >>> for m=0:19 // ... >>> powerseries_m = ((-1)^m / (factorial(m) * factorial(m + n))) * >>> (x/2)^(2*m); >>> powerseries = powerseries + powerseries_m; // sum the powerseries >>> end >>> >> Generally speaking, I think you'd better use the possibilities of vector >> calculation as much as possible, to have a faster calculation. >> >> The lines above could look like the following, assuming x is a column >> vector: >> >> m = 0:19; >> >> [x_mat, m_mat] = ndgrid(x, m); // rectangular matrices for group >> evaluation >> >> f = 1 ./(factorial(m) .* factorial(m + n)); >> >> f_mat = ndgrid(f, x)'; >> >> powerseries = sum((-1).^m_mat.*f_mat.*(x_mat/2).^(2*m_mat), "c"); >> >> However, this quite naive implementation is probably not accurate when x >> and m are high, >> for f would have some zeros (if m or m+n > 170) leading to zeros in >> powerseries, >> whereas f*(x/2)^(2m) might not be negligible. >> >> The reason why you should follow Nikolay's advice and use built-in >> functions, which usually use strong algorithms. >> >> -- >> Christophe Dang Ngoc Chan >> Mechanical calculation engineer >> This e-mail may contain confidential and/or privileged information. If >> you are not the intended recipient (or have received this e-mail in error), >> please notify the sender immediately and destroy this e-mail. Any >> unauthorized copying, disclosure or distribution of the material in this >> e-mail is strictly forbidden. >> _______________________________________________ >> users mailing list >> [email protected] >> http://lists.scilab.org/mailman/listinfo/users >> > Almost every numerical analysis textbook comprises a chapter on the > evaluation of Bessel functions, as for instance > Abramowitz ans Stegun, Handbook of mathematical functions, chapters > 9,10 (elegant use of recurrence relation) > Press et al., Numerical recipes, chapter 6 (rational approximations) > Enjoy! > > _______________________________________________ > users mailing list > [email protected] > http://lists.scilab.org/mailman/listinfo/users >
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