Flashcards
Series and sequence
Cards in this deck (12)
- 1What is the sequence theorem?Similar to series theorem
- 2When is a sequence / series convergent? What is absolute convergence?When it has a limit, i.e if it ends at a value
- 3and find n
- 4What is the sum of a geometric series?Replace r with Z since we are looking at complex series
- 5Why properties is there when discussing taylor series?In complex functions, any analytical function bound by circle of radius R centreing on zo can be expressed as a taylor series expansion
- 6What is the general form of taylor series around zo?
- 7—
- 8Express Exp(2z) in a taylor expansion and find its range and also for (Z^3)*Exp(2z)
- 9evaluate sin(z) and cos(z) as taylor expansions
- 10What is an isolated singularity?Its a singularity that is non analytic for a single point, but everywhere else in its NBH is analytic.
(Normal singularities can have a group of points in the NBH that are non analytic).
So isolated singularity is a special case - 11What is the point of the Laurent series?In cases where Zo isn't analytic, the Taylor series does not work. Laurent series however can be used as it includes negative powers. providing
- 12what is the equation for the laurent series?
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- Flashcards on Series and sequence, created by Elliot Bryce on 01/11/2018.
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- Elliot Bryce
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