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Re: Error in Bessel Zeros Package?

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  • Subject: [mg311] Re: [mg298] Error in Bessel Zeros Package?
  • From: Jerry Keiper <keiper>
  • Date: Sun, 11 Dec 1994 15:00:13 -0600

You don't say what you defined fd[ ] to be, but there is clearly
no zero at 6.00731:

In[35]:= fd[15.96641939477542]

Out[35]= 1.04083 10

In[36]:= fd[6.00731]

Out[36]= 0.0759842

Here is what I did:
nu = 3; l = 1.2;                             
jp[x_] = D[BesselJ[nu, x], x];
yp[x_] = D[BesselY[nu, x], x];
fd[x_] = jp[x] yp[l x] - jp[l x] yp[x];

Plot[fd[x], {x, 0, 20}]
Show[%, PlotRange -> {-1, 1}]

Plot[{jp[x] yp[l x], jp[l x] yp[x]}, {x, 0, 20}]

You will note that BesselJPrimeYPrimeJPrimeYPrimeZeros misses the
zero at

In[45]:= fd[2.730594863590175]

Out[45]= -2.77556 10

In fact it appears that it always misses the first zero.  This is
unfortunate and I will see what can be done to correct this.

Jerry B. Keiper
keiper at
Wolfram Research, Inc.

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