Residue - Definition and Overview

The term residue has several meanings in mathematics.Additionally, it has meaning in molecular biology.

In complex analysis, the residue is a complex number which describes the behavior of path integrals of a meromorphic function around a singularity. See residue (complex analysis).

In modular arithmetic, the residue of an integer n to base b is the remainder r after the largest multiple mb of b no greater than n has been subtracted from n (if n < 0, one adds multiples of b just sufficient to make the result non-negative). The residues modulo (to the base) b form a ring.

In molecular biology, particularly with enzymes, a residue refers to a specific amino acid. For example one might say: "the histadine residue is considered to be basic due to its imidazole ring". Note that a residue is different from a moiety, which, in the above example would consistute the imidazole ring or "the imidazole moiety".

See also

• Quadratic residue
• Norm residue symbol
• Poincaré residue
• Logarithmic residue
• Laurent series
• Leray residue
• Grothendieck residue
• Bott residue
• Heitsch residue
• Residues are not the same as residuals; see errors and residuals in statistics.