An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The application of → Cauchy's theorem to compute residues and poles, evaluate contour integrals, sum infinite series, and carry out related calculations.

→ calculus; → residue.

1) General: Something that remains after a process involving the removal of part of the original has been completed.
2) Math.: If f(z) is a → complex function, its residue at an isolated → singularity  z₀ is defined by the → integral (1/2πi) ∫f(z)dz taken along a simple closed curve interior to an annulus about z₀.

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.

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.

→ residue; → theorem.