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Concerning the Roots of J n ′( x ) N n ′( k x )− J n ′( k x ) N n ′( x ) = 0 J n ′ ( x ) N n ′ ( k x ) − J n ′ ( k x ) N n ′ ( x ) = 0

Concerning the Roots of J n ′( x ) N n ′( k x )− J n ′( k x ) N n ′( x ) = 0 J n ′ ( x ) N n ′ ( k x ) − J n ′ ( k x ) N n ′ ( x ) = 0 The relation J n ′( x ) N n ′( k x )− J n ′( k x ) N n ′( x ) = 0 J n ′ ( x ) N n ′ ( k x ) − J n ′ ( k x ) N n ′ ( x ) = 0 arises in certain resonant cavity problems having cylindrical symmetry. The first roots of this relation are presented here as a function of k for n = 1, 2, 3, 4. The M'Mahon relation does not allow calculation of the first roots despite statements to the contrary in several places. It is shown that the functions J n ′( x )/ N n ′( x ) J n ′ ( x ) ∕ N n ′ ( x ) have relative maxima at x = n except for n = 0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Physics American Institute of Physics
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