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

---------------------------------------------------

```

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