Assume that p is real. Let f(z) be a rational function with no poles on the positive real axis, and suppose thatlim z f(z) = lim zºf(z) = 0.z→0Z→∞Show that[² x²-1¹ f(x) dx =XP-πsin pRes{(-2)-¹1f(z)},where the sum is over all the poles of f(z).[Hint. Consider the integral f(-2)-¹ f(2)dz = f₁ ep−1) ¹(-2) f(z)dz, where I is a suitablecontour.]

As per the question we are given an importer integral and we have to find a generalized formula to…

Let f(z) be a rational function with no poles on the positive real axis, and suppose that lim Pf(z) lim zf(z) = 0. - 2-0 Show that [x²-¹ f(x) dx = XP-1 0 ㅠ sin p ΣRes{(-2)²-¹(2)}, where the sum is over all the poles of f(z). [Hint. Consider the integral (-2)-1 f(z)dz = fre(p-1) ln(-2) f(z)dz, where I is a suitable contour.]

Let f(z) be a rational function with no poles on the positive real axis, and suppose that lim Pf(z) lim zf(z) = 0. - 2-0 Show that [x²-¹ f(x) dx = XP-1 0 ㅠ sin p ΣRes{(-2)²-¹(2)}, where the sum is over all the poles of f(z). [Hint. Consider the integral (-2)-1 f(z)dz = fre(p-1) ln(-2) f(z)dz, where I is a suitable contour.]

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.6: Rational Functions

Problem 1E: If the rational function y=r(x) has the vertical asymptote x=2, then as x2+ , either y ______or y...

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