Biology Reference
In-Depth Information
195
and
Collecting terms with the same t
n
, we derive the following two recurrence
relations:
and
The second equation can also be written as:
On eliminating J
n-1
(x) and J
n+1
(x) from these two equations, we can verify
that J
n
(x) is one of the solutions of the following Bessel differential
equation:
The other solution is denoted by Y
n
(x) which is singular at x = 0.
If we consider t as the complex variable, Cauchy's integral theorem can be
applied to obtain the value of contour integral around a unit circle, i.e. t =
exp
in the counter-clock-wise direction of
Since
