bessel function with complex order

*To*: mathgroup at smc.vnet.net*Subject*: [mg46838] bessel function with complex order*From*: cirella at fis.uniroma3.it (cirella antonella)*Date*: Tue, 9 Mar 2004 19:57:56 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I'm looking for the definition used by Mathematica 4.0 to evaluate the Bessel function of the first kind with COMPLEX order. Generally Bessel function of the first kind are defined only for REAL order, but I have found that Mathematica can calculate Bessel function with COMPEX order. I would know: 1)how Mathematica defines Bessel function of first kind with COMPLEX order? 2)how Mathematica estimates real and imaginary part of Bessel function with COMPLEX order? I have searched in the Wolfram web site and in the references: listed below (cited in the Mathematica help pages) but I have not found these informations. http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html Abramowitz M., and Stegun I.A. (Eds.), 'Bessel Functions J and Y.' in 'Handbook of Mathematical functions with Formulas , Graphs , and Mathematical Tables' ,9th printing . New York : Dover ,pp.358 - 365. Arfken G., 'Bessel Functions of the First Kind,J(x)', 3rd ed., Orlando , FL: Academic Press, pp.573-591 and 591-596,1985. Watson G.N., 'A treatise on the Theory of Bessel Functions', 2nd ed. Cambridge, England. Could you clarify me the Mathematica's definition od this function? I need this information as soon as in your possibility. So, I greatly appreciate your contribution and I thank you in advance for your help. ---------------------------------------------------