Bessel Functions of the First Kind - The University of ...

X1 n=1 a n(z z 0)n; and if Cis any positively oriented simple closed curve in the complex plane containing z 0, then I C f(z)dz= 2ˇia 1: Therefore, if we apply this theorem to the generating function for the Bessel functions of integer order, we obtain I C e(x=2)(t 1=t) tn+1 dt= I X1 m=1 J m(x)tm n 1 dt= 2ˇiJ n(x); ................
................