In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.[1][2][3]
Contour integration is closely related to the calculus of residues,[4] a method of complex analysis.
One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods.[5]
Contour integration methods include:
direct integration of a complex-valued function along a curve in the complex plane;
application of the Cauchy integral formula; and
application of the residue theorem.
One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums.
^Stalker, John (1998). Complex Analysis: Fundamentals of the Classical Theory of Functions. Springer. p. 77. ISBN 0-8176-4038-X.
^Bak, Joseph; Newman, Donald J. (1997). "Chapters 11 & 12". Complex Analysis. Springer. pp. 130–156. ISBN 0-387-94756-6.
^Krantz, Steven George (1999). "Chapter 2". Handbook of Complex Variables. Springer. ISBN 0-8176-4011-8.
^Mitrinović, Dragoslav S.; Kečkić, Jovan D. (1984). "Chapter 2". The Cauchy Method of Residues: Theory and Applications. Springer. ISBN 90-277-1623-4.
^Mitrinović, Dragoslav S.; Kečkić, Jovan D. (1984). "Chapter 5". The Cauchy Method of Residues: Theory and Applications. Springer. ISBN 90-277-1623-4.
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