CAS PROJECT. sec, tan, arcsin. (a) Euler numbers. The
Chapter 15, Problem 15.4(choose chapter or problem)
CAS PROJECT. sec, tan, arcsin. (a) Euler numbers. The Maclaurin series E22 E44 (21) sec z = Eo - - z + - z - + ... 2! 4! defines the Elller numbers E2n- Show that Eo = 1, E2 = -I, E4 = 5, E6 = -61. Write a program that computes the E2n from the coefficient formula in (1) or extracts them as a list from the series. (For tables see Ref. [GRI]. p. 810. listed in App. 1.) (b) Bernoulli numbers. The Maclaurin series defines the Bernoulli numbers Bn. Using undeterminedcoefficients, show thatIBl = , B2 = - B3 = O.(23) 2 6I 1B4 = -- B5 = 0, B6 = - 30 42Write a program for computing Bn.(c) Tangent. Using (1), (2), Sec. 13.6, and (22), showthat tan z has the following Maclaurin series andcalculate from it a table of Bo, ... , B2O:2i 4
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