complex

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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Recall that sinh(2) = }(e² – e¯²).
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(i) Show that all the roots of sinh(z) are of the form zn = Nni, with n E Z.
(ii) Show that all the roots of sinh(z) are simple.
(iii) Find the residues of each singularity of 1/ sinh(z).
Transcribed Image Text:Recall that sinh(2) = }(e² – e¯²). | (i) Show that all the roots of sinh(z) are of the form zn = Nni, with n E Z. (ii) Show that all the roots of sinh(z) are simple. (iii) Find the residues of each singularity of 1/ sinh(z).
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