Estb. 1882

University of the Punjab

MATH-309 Complex Analysis – II

Singularity and Poles  Review of Laurent series
 Zeros, singularities
 Poles and residues Contour Integration
 Cauchy’s residue theorem
 Applications of Cauchy’s residue theorem Expansion of Functions and Analytic Continuation
 Mittag-Leffler theorem
 Weierstrass’s factorization theorem
 Analytic continuation Elliptic Functions
 Periodic functions
 Elliptic functions and its properties
 Weierstrass function φ(z)
 Differential equation satisfied by φ(z)
 Integral formula for (φ)z
 Addition theorem for (φ)z
 Duplication formula for (φ)z
 Elliptic functions in terms of Weierstrass function with the same periods
 Quasi periodic functions: The zeta and sigma functions of Weierstrass
 Jacobian elliptic functions and its properties
Credit hours/ Marks:- 3

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