Thank you.

Problem 2 [30 pts] ( Bessel's Equation and Bessel Fun ctions Bessel's equation is a second order differentis of applications including calculating heat conduction in a cylinder, establishing the radial Schrodinger equation to determine the shape of electron orbitals, finding diff jects (including DNA), and many more. day The actual differential equation is fo It can be shown that there is no "nice. expression for solutions to this comnation involving the common functions in Calculus (like polynomials exponentials, trigonometric functions, and logarithms). However, it is possible to use the differential equation to write down series representations for the solutions. In fifth tack when of It can be shown that the power series below is a solution to this equation Since we do not have a "nice" formula for / (c). wels not phils evaluate the function at a specific r-value, but we can try to approximate Ji() by using Taylor polynomials A. 8 pts Explain whether using higher order Taylor polynomials would in general provide better or worse approximations for , (10) than lower order ones. Make sure to show any computations that you need to establish your conclusion