Chapter 20, Problem 44P

Bessel functions often arise in advanced engineering analyses such as the study of electric fields. These functions are usually not amenable to straight forward evaluation and, therefore, are often compiled in standard mathematical tables. For example,

x	1.8	2	2.2	2.4	2.6
$J_1\left(x\right)$	0.5815	0.5767	0.556	0.5202	0.4708

Estimate $J_1$(2.1), (a) using an interpolating polynomial and (b) using cubic splines. Note that the true value is 0.568292.