8. Let two polynomials f (z) = ɑo + a,z + at all points z in a region R. Use the concept of a limit to show that m = n and that all coefficients + anz" and g(z) = bo + b,z + ·…· + bmz™ be equal ... {a} and {b}"-0 must be equal. Hint: Consider lim(f(z) – g(2)), lim(f(z) – g(z))/(z), etc. j=0 j=0 z→0 z→0

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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COmplex Analysis question, thanks for explaining in advance

8. Let two polynomials f(z) = ao + a,z + + anz" and g(z) = bo + b,z + … + bmz™ be equal
at all points z in a region R. Use the concept of a limit to show that m = n and that all coefficients
т
...
...
т
{a};-o and {b;};=0
n
must be equal. Hint: Consider lim (f(z) – g(z)), lim(f(z) – g(z))/(z), etc.
Transcribed Image Text:8. Let two polynomials f(z) = ao + a,z + + anz" and g(z) = bo + b,z + … + bmz™ be equal at all points z in a region R. Use the concept of a limit to show that m = n and that all coefficients т ... ... т {a};-o and {b;};=0 n must be equal. Hint: Consider lim (f(z) – g(z)), lim(f(z) – g(z))/(z), etc.
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