I see what you mean now. I think you have established that the maxima documentation http://maxima.sourceforge.net/docs/manual/en/maxima_16.html#SEC52 is wrong. I
've tested other J-Bessel values and some Y-Bessel values based on http://idlastro.gsfc.nasa.gov/idl_html_help/BESELJ.html The pari version of the J-Bessel fcn seems fine but the maxima version seems backwards. The Y Bessel function seems fine. The maxima version of the I-Bessel fcn is fine but the pari version seems backwards, based on http://idlastro.gsfc.nasa.gov/idl_html_help/BESELI.html That graph indicates the K-Bessel is backwards. Thanks for pointing this out. Before making changes, I want to email the maxima people and see what they say. +++++++++++++++++++++++++++++++++++= On 10/27/06, dt <[EMAIL PROTECTED]> wrote: > > First, > thank you for the quick replies. > > I did read the document at > http://modular.math.washington.edu/sage/doc/html/ref/module-sage.functions.special.html > before posting, but it didn't make it clear to me. I understood that > pari was the default, and that is fine with me. I realize now that > conventions were confusing me. > > OK, I see what is going on. I was wondering if argument order was > playing a role and I was instead calculating J(nu,x) nu=0..5 instead of > J(nu,x) x=0..5 > > I did indead do the plots you showed above that show zeroes. Why is > the position of x different in your last exampe? > > What is very confusing and non-intuitive to me at least is why the > conventions of the default bessel/pari and the 'maxima' option bessel > are reversed and are contradicted by the documentation. Bear with me: > > We know from tables or independant sources the Bessel J of order n=3.0 > has a value of 0 at z=0 and a value of 0.128 and z=2.0 > > The documentation cited above says: > bessel_J( nu, z, [alg=53], [prec=pari]) where alg='maxima' or 'pari' > > Now look at the following values from sage: > bessel_J(2.,3) #default is pari > 0.12894324947440206 > bessel_J(2.,3,'maxima') > 0.48609126058589119 > bessel_J(2.,3,'pari') > 0.12894324947440206 #this verfies default is pari > Note that 0.128.. is the expected value for J(nu=2,z=3.) so the maxima > value is 'wrong' see below > > bessel_J(3,2.,) > 0.48609126058589108 #same as maxima answer with reversed args > #i.e. this is bessel J (nu=2, z=3) > bessel_J(3,2.,'maxima') > 0.12894324947440211 #now we have the right answer > Therefore the argument order is reversed for 'maxima' option and if > fact, the default bessel has an order differenct from the documentation > or am I missing something elsewhere? > > bessel_J(0.,3) > 0.00000000000000000 #right > bessel_J(0.,3,'maxima') > -0.26005195490193339 #'wrong' > bessel_J(3,0.,'maxima') > 0.00000000000000000 #right > > So, the argument order given in the linked documentation is consistent > with maxima form but > not with the default or with 'pari' option. In fact, the examples in > that documentation: > " > sage: bessel_J(2,1.1) # last few digits are random > 0.136564153956658000 > sage: bessel_J(0,1.1) # last few digits are random > 0.719622018527510801 > sage: bessel_J(0,1) # last few digits are random > 0.765197686557966605 > " > > Do not work unless you reverse the order of the arguments or add the > "maxima" option. > > This is in fact what led me to believe a bug had been introduced. > > So the question is, is it intended that the default(Pari) bessel > functions (I've only looked at J in detail, I don't know if this is a > problem with the other bessel functions) have a different argument > convention than the ''maxima" option, and if so, the documentation > should describe this differences. As it stands now, something is > inconsistent. > > Sorry for the long post, I hope I've at least made my confusion clear. > > > -john > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
