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Unformatted text preview: Electromagnetic Theory I Problem Set 6 Due: 3 October 2011 21.a) Use the power series definition of the Bessel function J m ( x ) X k =0 ( ) k k !( k + 1 + m ) x 2 2 k + m (1) to derive the recursion formulas for Bessel functions: J m 1 ( x ) + J m +1 ( x ) = 2 m x J m ( x ) , J m 1 ( x ) J m +1 ( x ) = 2 dJ m ( x ) dx (2) b) Explain why these same recursion formulas are valid for N m , H (1) m , H (2) m . c) Using the definitions I m ( x ) = i m J m ( ix ) , K m ( x ) = i m +1 2 H (1) m ( ix ) (3) obtain the analogous recursion formulas for I m , K m . d)Use the power series defintion of J m , and the fact that ( z ) when z a nonpositive integer, to prove that J m ( x ) = ( ) m J m ( x ) when m is an integer. 22. In class, we obtained the empty space Green function in cylindrical coordiantes in the form 1 4  x x  = 1 4 X m = Z dkJ  m  ( k ) J  m  ( k ) e im (  ) e k  z z  (4) a) By adjusting the z dependent factors in this formula obtain the Dirichlet Green function...
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This note was uploaded on 09/25/2011 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Power

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