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Expand the given function in a Taylor series centered at the indicated point. f(z) = ez, zo = 51 Σ(Γ Give the radius of convergence R of the series. R=

Expand the given function in a Taylor series centered at the indicated point. f(z) = ez, zo = 51 Σ(Γ Give the radius of convergence R of the series. R=

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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Expand the given function in a Taylor series centered at the indicated point. f(z) = ez, zΟ = 51 Σ(Γ Give the radius of convergence R of the series. R =
Transcribed Image Text:Expand the given function in a Taylor series centered at the indicated point. f(z) = ez, zΟ = 51 Σ(Γ Give the radius of convergence R of the series. R =
Step2 b) j(z)= ² Zo 5i Taylor Sealen of f(x) centered at Zo {(z) = f(Zo) + (Z-Zo) f'(20) + (Z-Ze) {"(20) +----- f(x) = (² 2! 7 → ... sm (z)= e² ✓ mEN {"(20) 51 Taylor series of $(2) in given by f(2)= ei + .si 00 = é 6:28 pm (7-5ilesi + (3-51)" esi+ (2-5₁) ³ 21 un = [ (2-51) 3=0 Unt! (7-51)" mi L n760 = 3-700 50 (2-5; j+1 (n+1)! 3-51 3+1 Radius of convergence R = =+ = ∞ . AC 51% 7 (3-5;)") Was this solution √x 8
Transcribed Image Text:Step2 b) j(z)= ² Zo 5i Taylor Sealen of f(x) centered at Zo {(z) = f(Zo) + (Z-Zo) f'(20) + (Z-Ze) {"(20) +----- f(x) = (² 2! 7 → ... sm (z)= e² ✓ mEN {"(20) 51 Taylor series of $(2) in given by f(2)= ei + .si 00 = é 6:28 pm (7-5ilesi + (3-51)" esi+ (2-5₁) ³ 21 un = [ (2-51) 3=0 Unt! (7-51)" mi L n760 = 3-700 50 (2-5; j+1 (n+1)! 3-51 3+1 Radius of convergence R = =+ = ∞ . AC 51% 7 (3-5;)") Was this solution √x 8
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