can you please solve for 1 and 2 I'm stuck , it is Bessel function

PHY 302: Mathematical Methods in Physics Zoom Practice Exercises for Bessel Function (BF) module 1. Let's examine a subfamily of Bessel functions that will appear quite familiar to us. These are the solutions of Bessel's equation for the values m = 11/2, 43/2, 15/2, etc. Start with the case m = +1/2, and work out other examples for more practice, In each ease, use the Frobenius method; that is, start from scratch with a series solution of the type given in BF Eq: 16. Find and solve the indicial equation(s), determine the recursion relation for the coefficients, and identify the resulting series with known functions. 2. Show that each of the following is a form of Bessel's equation and obtain the solution in terms of Bessel functions. Hint: Begin by writing Bessel's equation with independent variable u and dependent variable f. Then rescale both of them in the following way: u = Cr and y = 1" f, where a, 8, and " are constants. Use the chain rule to computey' _dy/da andy" = dev/da' in terms of f and u. If you work this out correctly, you should find that the equations below are special cases for particular values of o, 3, G and m. If you are still stuck, see Handy Hint 13 for the derivation and Handy Hint 14 for some further worked examples. (a) y"+ my =0 (b) y" + 2n cy = 0 (c) my" + (2n + 1)7 + 27 -0 3. Using the Bessel function generating function (BF Tutorial Eqn. 51): (a) Show that F(a ty, h) = Fir hill, h). (b) Use this result to show that J. ( ly) = 2 (r),(y)