Use the Maciaurin series e = to obtain the Maclaurin series for the entire function f(z)=z

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 9
6.
Assume that fand g are entire finctions and that g(z)#0 for allzEC
Ifif(z)sg{z) for all zeC, hen prove that there is a constant C such thar
S(z)= Cg(z).
7.
Letf(z) 3z+2i. Find the maximum valne of f(z) on the disk z<1.
8.
Find the sum of the series
9.
Use the Maciaurin series e
to obtain the Maclaurin series for the
entire function f(z) = ze
10.
Write the Maclaurin series expansion for the function
S(z) =
z +4
4 1+(z /4)
and determine the radsus of convergence of inis series (tinat is the iargest vaiue of R
such that the series converges on the disk iz <R).
Transcribed Image Text:6. Assume that fand g are entire finctions and that g(z)#0 for allzEC Ifif(z)sg{z) for all zeC, hen prove that there is a constant C such thar S(z)= Cg(z). 7. Letf(z) 3z+2i. Find the maximum valne of f(z) on the disk z<1. 8. Find the sum of the series 9. Use the Maciaurin series e to obtain the Maclaurin series for the entire function f(z) = ze 10. Write the Maclaurin series expansion for the function S(z) = z +4 4 1+(z /4) and determine the radsus of convergence of inis series (tinat is the iargest vaiue of R such that the series converges on the disk iz <R).
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