Upgrading from:

NumericalMath`BesselZeros`

New function BesselJZero has been added to the built-in Mathematica kernel.
New function BesselYZero has been added to the built-in Mathematica kernel.

Evaluate the 5 th zero of the Bessel function numerically:

Version 5.2 << NumericalMath`BesselZeros`;
BesselJZeros[0, 5]

Similarly, evaluate the 1 st zero of the Bessel function numerically:

Version 5.2 << NumericalMath`BesselZeros`;
BesselYZeros[0, 1]

These functions were available in previous versions of Mathematica and are now available on the web at library.wolfram.com/infocenter/MathSource/6777:

BesselJPrimeYJYPrimeZeros
BesselJPrimeYJYPrimeZerosInterval
BesselJPrimeYPrimeJPrimeYPrimeZeros
BesselJPrimeYPrimeJPrimeYPrimeZerosInterval
BesselJPrimeZeros
BesselJPrimeZerosInterval
BesselJYJYZeros
BesselJYJYZerosInterval
BesselJZeros
BesselJZerosInterval
BesselYPrimeZeros
BesselYPrimeZerosInterval
BesselYZeros
BesselYZerosInterval