Chem Differential Eq HW Solutions Fall 2011 79

Chem Differential Eq HW Solutions Fall 2011 79 - Hence J (...

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Section 4.9 Integral Formulas and Asymptotics for Bessel Functions 79 Solutions to Exercises 4.9 1. We have J 0 ( x )= 1 π ± π 0 cos ( - x sin θ ) = 1 π ± π 0 cos ( x sin θ ) dθ. So J 0 (0) = 1 π ± π 0 =1 . For n ± =0 , J n ( x )= 1 π ± π 0 cos ( - x sin θ ) ; so J n (0) = 1 π ± π 0 cos nθ dθ =0 . 5. All the terms in the series 1= J 0 ( x ) 2 +2 ² n =1 J n ( x ) 2
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Unformatted text preview: Hence J ( x ) 2 1 | J ( x ) | 1 and, for n 2, 2 J n ( x ) 2 1 | J n ( x ) | 1 2 ....
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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