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consider the integral A cot az dz Sc (a + z)² Equation 1 Here C is a circle of large radius. A cot a2 dz = 2ni 1 - n°cosec²ra Jc (a + z)²' (a + n)² Equation 2 where N equals the integer part of R.This indicates that when R → ∞ , N → 0 as well. 1. Now recalling the fact that C is a circle (the contour) whose radius is very large (i.e R → ∞) show that the left hand side of Equation 2 is 0 2.Finally, using your results from 2 , show that 1 (a + n)² sin Ta n=-00

consider the integral A cot az dz Sc (a + z)² Equation 1 Here C is a circle of large radius. A cot a2 dz = 2ni 1 - n°cosec²ra Jc (a + z)²' (a + n)² Equation 2 where N equals the integer part of R.This indicates that when R → ∞ , N → 0 as well. 1. Now recalling the fact that C is a circle (the contour) whose radius is very large (i.e R → ∞) show that the left hand side of Equation 2 is 0 2.Finally, using your results from 2 , show that 1 (a + n)² sin Ta n=-00

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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consider the integral A cot az dz Sc (a + z)² Equation 1 Here C is a circle of large radius. A cot a2 dz = 2ni 1 - n°cosec²ra Jc (a + z)²' (a + n)² Equation 2 where N equals the integer part of R.This indicates that when R → ∞ , N → 0 as well. 1. Now recalling the fact that C is a circle (the contour) whose radius is very large (i.e R → ∞) show that the left hand side of Equation 2 is 0 2.Finally, using your results from 2 , show that 1 (a + n)² sin Ta n=-00
Transcribed Image Text:consider the integral A cot az dz Sc (a + z)² Equation 1 Here C is a circle of large radius. A cot a2 dz = 2ni 1 - n°cosec²ra Jc (a + z)²' (a + n)² Equation 2 where N equals the integer part of R.This indicates that when R → ∞ , N → 0 as well. 1. Now recalling the fact that C is a circle (the contour) whose radius is very large (i.e R → ∞) show that the left hand side of Equation 2 is 0 2.Finally, using your results from 2 , show that 1 (a + n)² sin Ta n=-00
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