Page 130 - Essentials of applied mathematics for scientists and engineers
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book Mobk070 March 22, 2007 11:7
120 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS
We can formally differentiate the above equation n times with respect to z 0 and find an
extension as
n! f (z)
f (n) (z 0 ) = dz (7.29)
2πi C (z − z 0 ) n+1
Problems
1. Show that
(a) sinh z = sinh x cos y + i cosh x sin y
(b) cos z = cos x cosh y − i sin x sinh y
and show that each is entire.
2. Find all of the values of
√ 3
(a) (−1 + i 3) 2
1
(b) 8 6
3. Find all the roots of the equation
sin z = cosh 4
4. Find all the zeros of
(a) sinh z
(b) cosh z
