C b от 3 Ju(x)= a) substitute v=m n=o (-1) (-1)" for an integer n (n+1)= [(n) = nl n! [(m+n+1) 2 20+vm 2n+v m and n are integers So [(m+n+1)=(any)! (m+n)+1)=(m+n)! antm X 8 no 8 (-1)" 22n+mn! (m+n)! n=O (-1)" 220-mn! (min n-m)! 2n-m X The Bessel function of the first kind of order v (where v is a positive real number) can be written as the power series (-1)* 2n+v Jv(x)=Σn=0T(n+1)(v+n+1) a) Write down the power series for the special case v = m, where m is a positive integer. Simplify the coefficients in this power series as much as possible b) Write down the power series for v = -m. c) Show that the first coefficients of the power series in part (b) are zero. Calculate the first non-zero coefficient.