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Re: Simplifying Bessel Functions


Aaron Fude wrote:

> What do I need to do to make mathematica recognize the following
> expression as zero:
> 
> BesselJ[0, BesselJZero[0, n]]

You could add an up-value to BesselJZero. Below, we unprotect the 
built-in symbol BesselJZero and add the new rule thanks to 
*TagSetDelayed*  (shortcut "/: :=", w/o the quotes).

   In[1]:= BesselJ[0, BesselJZero[0, n]]

           Unprotect[BesselJZero];
             BesselJZero /: BesselJ[0, BesselJZero[0, n_]] := 0
           Protect[BesselJZero];

           BesselJ[0, BesselJZero[0, n]]

Out[1]= BesselJ[0, BesselJZero[0, n]]

Out[5]= 0

(Note that the above definition is very broad since it works for any n, 
not just for positive integers.)

HTH,
-- Jean-Marc


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