(a) Experiment with (14) for integer n. Using graphs, find out from which x = x n on the curves of (11) and (14) practically coincide. How does x n change with n? (b) What happens in (b) if n = ±1/2? (Our usual notation in this case would be v.) (c) How does the error of (14) behave as
Chapter 5, PROBLEM SET 5.4 #12
(a) Experiment with (14) for integer n. Using graphs, find out from which x = xn on the curves of (11) and (14) practically coincide. How does xn change with n?
(b) What happens in (b) if n = ±1/2? (Our usual notation in this case would be v.)
(c) How does the error of (14) behave as a function of x for fixed n? [Error = exact value minus approximation (14).]
(d) Show from the graphs that J0(x) has extrema where J1(x) = 0. Which formula proves this? Find further relations between zeros and extrema.
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