Page 96 - DMTH402_COMPLEX_ANALYSIS_AND_DIFFERENTIAL_GEOMETRY

Unit 8: Series

12. Find the limit of Notes

j
 n z 
  . 

 j 1 j 

For what values of z does the series converge?
 n 
j
13. Find a power series  c (z 1)  such that

 j 
 j 0 

1  c (z 1) ,for|z 1| 1.
j
z   j   
j 0



n
j
14. Find a power series  c (z 1)  such that

 j 
 j 0 


log z =  c (z 1)j,for|z 1| 1.



j
j 0

Answers: Self Assessment
1. sequence 2. |a – a | < 
m
n
3. complex functions 4. partial sums
 j
j
5. power series. 6.  g(z)S(z)dz   c g(z)(z z ) dz.

0
C j 0 C

8.10 Further Readings
Books Ahelfors, D.V. : Complex Analysis
Conway, J.B. : Function of one complex variable
Pati,T. : Functions of complex variable
Shanti Narain : Theory of function of a complex Variable
Tichmarsh, E.C. : The theory of functions
H.S. Kasana : Complex Variables theory and applications

P.K. Banerji : Complex Analysis
Serge Lang : Complex Analysis
H.Lass : Vector & Tensor Analysis

Shanti Narayan : Tensor Analysis
C.E. Weatherburn : Differential Geometry
T.J. Wilemore : Introduction to Differential Geometry
Bansi Lal : Differential Geometry.

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