(a) If f(2) is entire and zo E C, then f(2) is represented by a Taylor series centered at zo and converges for all z E C. (b) Theorem on Taylor series guarantees that log z can be expanded in positive powers of z. (c) The function f(2) is analytic at 20 if and only if it has Taylor series expansion in powers of z (d) A function analytic at 2o may have two different Taylor series expansions centered at %o- Zo convergent in some open disk centered at z0. analytic at zo and f(k) (2o) = 0 for k = 0, 1,2,..., then f(2o) (e) If f z in some open disk centered at zo. = 0 for all

(a) If f(2) is entire and zo E C, then f(2) is represented by a Taylor series centered at zo and converges for all z E C. (b) Theorem on Taylor series guarantees that log z can be expanded in positive powers of z. (c) The function f(2) is analytic at 20 if and only if it has Taylor series expansion in powers of z (d) A function analytic at 2o may have two different Taylor series expansions centered at %o- Zo convergent in some open disk centered at z0. analytic at zo and f(k) (2o) = 0 for k = 0, 1,2,..., then f(2o) (e) If f z in some open disk centered at zo. = 0 for all

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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