i. Write down the McLaurin series expansion of f(z). 11. Deduce the McLaurin series expansion of f (z) = sin z iii. Hence, deduce the McLaurin series expansion of f(z) = cos (z -- 4.
i. Write down the McLaurin series expansion of f(z). 11. Deduce the McLaurin series expansion of f (z) = sin z iii. Hence, deduce the McLaurin series expansion of f(z) = cos (z -- 4.
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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Transcribed Image Text:Write down the McLaurin series expansion of f (z).
ii.
Deduce the McLaurin series expansion of
f (z) = sin z
...
Hence, deduce the McLaurin series expansion of
111.
f (z) =
= cos ( z
-
Transcribed Image Text:Q2.
Test the following complex series and Determine whether the series are convergent or
а.
divergent.
i.
Un =
(1+n)n2
a+1
(a+1)(2a+1)
(a+1)(2a+1)(3a+1)
E Un
= 1+
b+1
--+; a, b E R.
11.
(b+1)(2b+1)
(b+1)(2b+1)(3a+1)
b. Find the radius of convergence of the following series.
3z2
= 2z +
8.
4z
5z4
E un
1.
27
64
(1+sin
Un
11.
zn
n
n+sin an
111.
Un =
zn
1
iv.
= "n
32n
Consider the following complex function.
с.
f (z) = e2
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