24.1. Find the first four terms of the power series expansions about z = 0 of the following functions: %3D 1 1 (a). z2 + 3 (b). 22 – 2' (c). 2 - 2 (d). 22 – 2z + 2' (e). sec z.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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24.1. Find the first four terms of the power series expansions about
z = 0 of the following functions:
1
1
(a).
z2 +3
(b).
z2 – 2
(c). (d). 2 (e). sec z.
2 –
2z +
24.2. Show that, for any constant zo E C,
(z – z0)i
j!
(а). е — е*0
|2| < o0. Hence, deduce that ež1+22 = e%i e2.
j=0
(b). sin z = sin zo cos(z - zo) + cos zo sin(z – zo).
Transcribed Image Text:24.1. Find the first four terms of the power series expansions about z = 0 of the following functions: 1 1 (a). z2 +3 (b). z2 – 2 (c). (d). 2 (e). sec z. 2 – 2z + 24.2. Show that, for any constant zo E C, (z – z0)i j! (а). е — е*0 |2| < o0. Hence, deduce that ež1+22 = e%i e2. j=0 (b). sin z = sin zo cos(z - zo) + cos zo sin(z – zo).
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