Let z be a complex number, f be a function in z and g(z)=(if(2))/2. Which among the following statements is (are) true? * If the Laurent series of f around 0 doesn't O contain negative powers of z then f is analytic. If f is entire then it is not necessary that g has a Maclaurin expansion. If the residue of f at z=0 is equal to 0 then f is analytic at 0. None of these All of these

Let z be a complex number, f be a function in z and g(z)=(if(2))/2. Which among the following statements is (are) true? * If the Laurent series of f around 0 doesn't O contain negative powers of z then f is analytic. If f is entire then it is not necessary that g has a Maclaurin expansion. If the residue of f at z=0 is equal to 0 then f is analytic at 0. None of these All of these

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

1. Find the Fourier series of f(x) = x² F(-2)? - x defined for -2 ≤ x ≤ 2 if ƒ (x + 4). What is BONUS: Truncate the series to n = 3, 5, 10. Plot the 3 series in one graph. What is F(−2) for each?
{In(8n +1) – In(4n +5)} 20. a. 2 b. 0 c. In(2) d. In(5) e. Divergent
Question 3 Use Taylor series to evaluate the limit. lim x2(etx² - 1) X-00 O -4 -1 O 4 O 1
(b) Let a, be a sequence of complex numbers such that E lanl < o. Suppose that Σ 2 a,k" = 0 for k = 1,2, .... n=0 Prove that a, = 0 for all n.
5. Expand the following function in Fourier series where f(x) = { show that f(x): = + 22-1 [(-1)^-1 nπ ·cos nxX- [1 when -1
1) e(x- 2)" student solution for (T.S): n=0 2" n! a) e?x b) et c) e? d) sin 2x 2)What are the first four terms of the Taylor series for e* when a = 1? e- =e+e(x-1) + 늘c(-1)2 A. +e(x- 1)3 +... e-= = e – e(x – 1) + e(x – 1)? B. -e(x – 1)3 +... e = !+(- 1) + (z – 1)2 c + (= – 1)° + .. c= = !- (x – 1) + (x – 1)? D- (E – 1)* + ... | 3)What is the x term in the Taylor expansion for xe* when a = 0? A) B) C)F DY 4) What is the fourth term in the Taylor expansion for 1 when a = 1 ? A)2(1 – 2) B)2(z – 1)° C)(1- z) D )(7- 1)
What is the expansion of f (x) = 1/1-x
3) Maclaurin expansion of 4th order of f(x) = 3xsinhx + cos√√6-1
Let X= {ne 7 /n=2k for some odd integer & f F = {ne z/n=4k for some integer *} E = {nEX/ n is even } 1. Prove that Fc I 2. Prove that XEnF
[0 when - 7