Abstract
This chapter discusses integration in the complex plane. It is possible to study completely the properties of the various sines and their similarities and differences if they are treated as functions of a complex variable t= σ+ iτ, where σ and τ are real numbers and i is the imaginary unit. If an integrand is a rational function and the square root of a polynomial of no higher than fourth degree, in that case, such an integral is called an elliptic integral, provided the integrand does not reduce to a rational function.
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