Question

Please question 4 complex analysis course

2:30 PM Wed May 1 Not Secure files.isec.pt 301 4.3 Evaluation of Definite Integrals where (w) adr. We know from the Gaussian integral that 1(0) V2π, so our conclusion will follow if we can show that I(W) 1(0) for every real w. To see this, consider the integral of g(z) = e-z2/2 around a rectangle Г = 1 + 11 + 111 + IV such as that shown in Figure 4.3.10 IV Figure 4.3.10: Contour for the Fourier transform of the normal probability function. We know that 0g g+ugIvg since g is an entire function. Along the horizontal sides where andzriw, we haveJg-I(0) and9-1() as Ro. Our conelusion will follow as soon as we show that g and Jy g tend to 0 as R- o. We do that for the right side, II, and for w>0 The other cases are similar This establishes our assertion Exercises 1. Evaluate llint: Consider /: Tdz and apply L" sin r dz-; 2. Prove that Proposition 4.3.11 for 0b<a 3. Evaluate (a + bcos θ)2 0 d.a A. Evaluate 1+

Answer 1

enu ejrele 2 eurthin c. 6 どれ

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