What is a difference between a Taylor polynomial and the Taylor series for a function f at a point ?
A function f with Taylor polynomial and the Taylor series
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 where p is a non-negative integer
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