(a) Write a program that gives and graphs partial sums of (15). Apply it to Probs. 5 and 6. Do the graphs show that those partial sums satisfy the boundary condition (3a)? Explain why. Why is the convergence rapid?

(b) Do the tasks in (a) for Prob. 4. Graph a portion, say, 0

(c) Do the tasks in (b) for functions of your choice.

Data from Prob. 5

Represent f (x, y) by a series (15), where

f (x, y) = y, α = b = 1

Data from Prob. 6

Represent f (x, y) by a series (15), where

f (x, y) = x, α = b = 1

1.0 0.83 0.41 0.1 0.2 3 0.33 0.44 0.5 0.5 0.4 0.3 0.2 0.1