Show that, if m is a positive integer, then Jm (x) = x m

Chapter 15, Problem 15.55

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Show that, if m is a positive integer, then Jm (x) = x m 2m1 (m + 1/2) /2 0 cos2m ( ) cos(x sin( )) d. This expression is called Poissons integral. Hint: Put t = sin( ) in Hankels integral, 22

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