The second-order differential equation
where p is a non-negative integer, arises in many applications in physics and engineering, including one model for the vibration of a beaten drum. The solution of the differential equation is called the Bessel function of order p, denoted by . It may be shown that is given by the following power series in x :
What is the interval of convergence for ?
The series is converges for all values of x.
An expression is given as
We have to do ratio test first for the absolute convergence,
It implies that
Calculate for k tending to infinity,
Limit is zero independently of x. So the series is converges for all values of x.
94% of StudySmarter users get better grades.Sign up for free