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"5. By Exercise 94, Ta(x) converges for (x|

By Exercise 94, Ta(x) converges for IXI < 1, but we do not yet know Whether Ta(x) = (1 -F x)a. (a) Verify the identity a) n (b) Use (a) to show that y = Ta(x) satisfies the differential equation (l + = ay with initial condition y(0) (c) Prove Ta(x) = (1 + xy for IXI < 1 by showing that the derivative of Ta(x) the ratio is zero.