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Integral of Sinc Function Squared Over The Real Line Explanation: (1): Expand sin2x in terms of complex exponentials and shift the pole upwards (2): Split the integral into 2 Integrate the first along a semicircle in the uhp, and the second along a semicircle in the lhp The second integral = 0 since it encloses no poles Alternatively, one may use the fact that ∫∞ 0 tn−1e−xtdt = Γ(n) xn
How does a complex exponential turn into the sinc function? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Derivative of sinc function - Mathematics Stack Exchange Use the Taylor series expansion as mentioned in the comments to get: sinc(x) = sin x x = −∑∞ k=0 (−x)2k+1 (2k+1)! x = −∑k=0∞ (−1)2k+1(x)2k (2k + 1)! = 1 − x2 3! + x4 5! −⋯ which is infinitely often differentiable at 0 You'll get dm dxmsinc(x)|x = 0 = {(− 1)m (m + 1) if m is even case 0 if m odd Because the product of