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6. Determine all fun et ions f analytic in |z| < 1 and satisfying k+ k2 1+k2 k = 2,3, 4, ...

6. Determine all fun et ions f analytic in |z| < 1 and satisfying k+ k2 1+k2 k = 2,3, 4, ...

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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Do 6 in detail and answer is attached

H) ZEROS AND UNIQUENESS 1. а) 3, b) 3. a) z = ±i, order 1, b) z = e(#/4+k#/2), k = 0, 1, 2, 3, order 1, c) z = 0, order 3; z = km, k E Z \ {0}, order 1, d) z = 2kn, k E Z, order 2, e) z = i(x/4+ ka/2), k e Z, order 1, f) z = 1, order 1. 2. 5. No. It is impossible by the uniqueness principle. z+1 6. f(2) = 22+ 1'
Transcribed Image Text:H) ZEROS AND UNIQUENESS 1. а) 3, b) 3. a) z = ±i, order 1, b) z = e(#/4+k#/2), k = 0, 1, 2, 3, order 1, c) z = 0, order 3; z = km, k E Z \ {0}, order 1, d) z = 2kn, k E Z, order 2, e) z = i(x/4+ ka/2), k e Z, order 1, f) z = 1, order 1. 2. 5. No. It is impossible by the uniqueness principle. z+1 6. f(2) = 22+ 1'
5. Is there any fun ction f, analytic in |z| < 1, su ch that and () 1 k = 1,2, 3, ...? 2k 2k 6. Determine all fun ctions f analytic in |z| < 1 and sati sfying k + k? k = 2,3, 4, ... 1+k²'
Transcribed Image Text:5. Is there any fun ction f, analytic in |z| < 1, su ch that and () 1 k = 1,2, 3, ...? 2k 2k 6. Determine all fun ctions f analytic in |z| < 1 and sati sfying k + k? k = 2,3, 4, ... 1+k²'
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