# Bessel functions often arise in advanced engineering analyses such as the study of electric fields.x1.82.02.22.42.6 J1(x)0.58150.57670.55600.52020

Bessel functions often arise in advanced engineering analyses such as the study of electric fields. Here are some selected values for the zero-order Bessel function of the first kind.
$$\begin{array}\\ x&1.8&2.0&2.2&2.4&2.6\\ J_1(x)&0.5815&0.5767&0.5560&0.5202&0.4708 \end{array}$$
Estimate $$J_1(2.1)$$ using third- and fourth-order interpolating polynomials. Determine the percent relative error for each case based on the true value, which can be determined with MATLAB’s built-in function besselj.

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Bertha Stark
y = 0.5743, 0.56834, 0.56829, 0.5683
ea3 = 0.00081573
ea4 = 0.0020712