PROBLEM 14E

Verify that the formulas for the Bessel functions J1/2(t),Y1/2(t) do indeed solve equation (16).

Solution

Step 1 of 5</p>

In this problem we have to verify that the formulas for the bessel functions solve the given equation.

Step 2 of 5</p>

Verifying the first formula

Neglecting constant we can consider the formula as

Differentiating with respect to t, we get

,

Bessel equation of order

Step 3 of 5</p>

Substituting the formula in the equation we get

Thus is the solution.