Develop the Laurent series of the function: 1 = = (z − a) (z — b) Centered at z = a, and in the annular region: |a| < |2|< b| 23-234 (b) --- 9 (2) = b 2+1 [n=0 n=0 an+1 +E; n= bn+1 Is: [3+2376 (c) (d) [n=0 an+1 n=0 0 ₂+1 ∞ fn+1] Σ + Ln=0 =02n a-b an+1

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Q: z2-1 (b) Obtain the Taylor's series to represent the function in the region (z+2)(Z+3) |z|< 2.

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Q: Let f (x) = 2021x* + 4x? + 12. Let f(1) Σα P (). l=0 be the Legendre series of f(x), where the Pe(x)…

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Q: 8) For this problem, consider the function f(x) = e". (a) Find P3(x), the third-degree Maclaurin…

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Q: (14) Use a Laurent series to find the residue of 2 f(z) = (z+3) sin z + 3 at the singularity z = -3.…

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Q: Σ H=I Τ n(n+1)

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Q: (-1)"4"+1,n+1 3n+1(n +1) In this problem, we investigate the power series n=0 (a) Show that…

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Q: Use the definition to find the Taylor series centered at c = 1 for the function f(x) = Select one: 6…

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Q: Use a Laurent series to find the indicated residue. f(z) e-z (z-4)² -; Res (f(z), 4)

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