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Find the power series of the function f(z) = sin(2z) with centre 7/3. Find the power series of the function f(z) = e(52) with centre i/3.

Find the power series of the function f(z) = sin(2z) with centre 7/3. Find the power series of the function f(z) = e(52) with centre i/3.

Advanced Engineering Mathematics
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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Find the power series of the function f(2) = sin(2z) with centre 7/3. Find the power series of the function f(z) = e(52) with centre i/3. Find the power series of the function f(2) = cos(z) with centre 1.
Transcribed Image Text:Find the power series of the function f(2) = sin(2z) with centre 7/3. Find the power series of the function f(z) = e(52) with centre i/3. Find the power series of the function f(2) = cos(z) with centre 1.
Expert Solution
Step 1

We will use taylor series at x=a

The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number a is the power series

f(x)= f(a) +f'(a)1!(x-a) +f''(a)2!(x-a)2+f'''(a)3!(x-a)3+.......∞

where n! denotes the factorial of n and fn (a)  denotes the nth derivative of f evaluated at the point a. 

in summetion form it can be written as 

f(x)=∑n=0∞fn(a)n!x-an

Note : Only one question are allowed to be solved at a time I have solved two , hope it will be helpfull

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