Question 1 entire function defined by For nonnegative integer k, the Bessel function of order k...

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Question 1 entire function defined by For nonnegative integer k, the Bessel function of order k is an Je(2) = (-1)"zk+2n n!(k + n)!2k+2n ° n=0 Show that J satisfies the differential equation (1-) -. k2 Jk = 0. z2 J" + -J + What type of singularity does g(2) = Jk() have at z = 0? What is res(g(2), 0)? Question 1 entire function defined by For nonnegative integer k, the Bessel function of order k is an Je(2) = (-1)"zk+2n n!(k + n)!2k+2n ° n=0 Show that J satisfies the differential equation (1-) -. k2 Jk = 0. z2 J" + -J + What type of singularity does g(2) = Jk() have at z = 0? What is res(g(2), 0)?