The imaginary unit is denoted by i. From the Taylor series around the origin of the function exp(z) calculate the Taylor series around the origin of the function cosine. (a) For what values of Z ∈ C do we have point convergence? (b) Compute directly the Taylor series around the origin of the function cos(z) by the formula and confirm that both Taylor series expansions coincide.
The imaginary unit is denoted by i. From the Taylor series around the origin of the function exp(z) calculate the Taylor series around the origin of the function cosine. (a) For what values of Z ∈ C do we have point convergence? (b) Compute directly the Taylor series around the origin of the function cos(z) by the formula and confirm that both Taylor series expansions coincide.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 20E
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The imaginary unit is denoted by i.
From the Taylor series around the origin of the function exp(z) calculate the Taylor series around the origin of the function cosine.
(a) For what values of Z ∈ C do we have point convergence?
(b) Compute directly the Taylor series around the origin of the function cos(z) by the formula and confirm that both Taylor series expansions coincide.
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