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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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