calculus of residues
Fr.: calcul des résidus
The application of → Cauchy's theorem to compute residues and poles, evaluate contour integrals, sum infinite series, and carry out related calculations.
Something that remains after a process involving the removal of part
of the original has been completed.
M.E., from O.Fr. residu, from L. residuum "a remainder," neuter of residuus "remaining, left over," from residere "to remain behind."
Munak, from mun-, dialectal variant of mân-/mândan "to remain" (e.g., Farizani mundä, Gazi mun-, Khunsâri mûn-, Natanzi, Semnâni -mund, Yghnobi mun-), Mid.Pers. mân-/mândan "to remain, to stay;" O.Pers. mān "to remain, dwell;" Av. mān- "to remain, dwell;" cognate with E. → remain; + relation/diminution suffix -ak.
Fr.: théorème des résidus
The theorem stating that the value of the line integral of a complex function, taken along a simple closed curve encircling a finite number of isolated singularities, is given by 2πi times the sum of the residues of the function at each of the singularities.