# Functions and operators

Named functions, operator names, and limits.

https://texform.dev/latex/topics/functions

This topic has 74 commands from the physics, base, and ams packages. Commands show whether MathJax, KaTeX, and XeTeX render them. Entries are ordered by how often they appear in corpus formulas.

Packages: physics (48), base (36), ams (8).

| Name | Kind | Definition | Packages | MathJax | KaTeX | XeTeX | Frequency |
| --- | --- | --- | --- | --- | --- | --- | --- |
| [\\operatorname](https://texform.dev/latex/commands/operatorname) | command | Used to create named math operators such as \operatorname{sgn} or limit-style operators via \operatorname*{lim} when no predefined operator macro exists. | ams | full | full | full | 3.58% |
| [\\log](https://texform.dev/latex/commands/log) | command | Used for logarithms in algebra, calculus, asymptotics, and applied mathematics | base, physics | full | full | full | 3.19% |
| [\\exp](https://texform.dev/latex/commands/exp) | command | Used for the exponential function in analysis, calculus, and differential equations | base, physics | full | full | full | 2.30% |
| [\\cos](https://texform.dev/latex/commands/cos) | command | Used for cosine in trigonometric formulas, identities, and Fourier-style calculations | base, physics | full | full | full | 2.01% |
| [\\sin](https://texform.dev/latex/commands/sin) | command | Used for sine in trigonometric formulas, identities, and calculus | base, physics | full | full | full | 1.93% |
| [\\max](https://texform.dev/latex/commands/max) | command | Used for the maximum of a set or expression | base | full | full | full | 1.78% |
| [\\lim](https://texform.dev/latex/commands/lim) | command | Used for mathematical limits | base | full | full | full | 1.73% |
| [\\sup](https://texform.dev/latex/commands/sup) | command | Used for the supremum of a set or mathematical expression | base | full | full | full | 1.56% |
| [\\min](https://texform.dev/latex/commands/min) | command | Used for the minimum of a set or expression | base | full | full | full | 1.52% |
| [\\ln](https://texform.dev/latex/commands/ln) | command | Used for the natural logarithm in calculus, analysis, and applied mathematics | base, physics | full | full | full | 1.42% |
| [\\inf](https://texform.dev/latex/commands/inf) | command | Used for infimum notation in analysis, often with subscripts indicating the domain or index set. | base | full | full | full | 0.66% |
| [\\det](https://texform.dev/latex/commands/det) | command | Used for the determinant of a matrix | base, physics | full | full | full | 0.48% |
| [\\dim](https://texform.dev/latex/commands/dim) | command | Used for dimension as a named operator in linear algebra and geometry | base | full | full | full | 0.31% |
| [\\cosh](https://texform.dev/latex/commands/cosh) | command | Used for hyperbolic cosine in analysis, differential equations, and mathematical physics | base, physics | full | full | full | 0.28% |
| [\\sinh](https://texform.dev/latex/commands/sinh) | command | Used for hyperbolic sine in analysis, differential equations, and mathematical physics | base, physics | full | full | full | 0.27% |
| [\\limsup](https://texform.dev/latex/commands/limsup) | command | Used for limit superior notation in analysis, ergodic theory, and probability. | base | full | full | full | 0.27% |
| [\\liminf](https://texform.dev/latex/commands/liminf) | command | Used for limit inferior notation in analysis, ergodic theory, and probability. | base | full | full | full | 0.19% |
| [\\tan](https://texform.dev/latex/commands/tan) | command | Used for tangent in trigonometric formulas, identities, and calculus | base, physics | full | full | full | 0.19% |
| [\\arg](https://texform.dev/latex/commands/arg) | command | Used for the argument or phase of a complex number in complex analysis | base | full | full | full | 0.19% |
| [\\Pr](https://texform.dev/latex/commands/Pr) | command | Used for the probability of an event | base, physics | full | full | full | 0.17% |
| [\\deg](https://texform.dev/latex/commands/deg) | command | Used for degree as a named operator in algebra, graph theory, and related notation | base | full | full | full | 0.17% |
| [\\tanh](https://texform.dev/latex/commands/tanh) | command | Used for hyperbolic tangent in analysis, differential equations, and related formulas | base, physics | full | full | full | 0.16% |
| [\\pmod](https://texform.dev/latex/commands/pmod) | command | Used in congruence notation to add a parenthesized modulus such as x \equiv y \pmod{n} | base | full | full | full | 0.14% |
| [\\ker](https://texform.dev/latex/commands/ker) | command | Used for kernel as a named operator in linear algebra and algebra | base | full | full | full | 0.10% |
| [\\mod](https://texform.dev/latex/commands/mod) | command | Used in modular arithmetic to write an unparenthesized modulus qualifier after an expression | base | full | full | none | 0.09% |
| [\\arctan](https://texform.dev/latex/commands/arctan) | command | Used for inverse tangent in trigonometric identities, angle formulas, and calculus | base, physics | full | full | full | 0.09% |
| [\\cot](https://texform.dev/latex/commands/cot) | command | Used for cotangent in trigonometric identities and analytic derivations | base, physics | full | full | full | 0.08% |
| [\\bmod](https://texform.dev/latex/commands/bmod) | command | Used for a standalone 'mod' operator with binary-operator spacing in modular arithmetic expressions | base | full | full | full | 0.07% |
| [\\coth](https://texform.dev/latex/commands/coth) | command | Used for hyperbolic cotangent in analysis and specialized mathematical formulas | base, physics | full | full | full | 0.05% |
| [\\gcd](https://texform.dev/latex/commands/gcd) | command | Used for greatest-common-divisor notation in number theory and algebra. | base | full | full | full | 0.04% |
| [\\arccos](https://texform.dev/latex/commands/arccos) | command | Used for inverse cosine in trigonometric formulas and calculus | base, physics | full | full | full | 0.04% |
| [\\arcsin](https://texform.dev/latex/commands/arcsin) | command | Used for inverse sine in trigonometric formulas and calculus | base, physics | full | full | full | 0.03% |
| [\\varprojlim](https://texform.dev/latex/commands/varprojlim) | command | Typesetting the variable-style inverse-limit operator in algebra, topology, and related areas. | ams | full | full | full | 0.02% |
| [\\sec](https://texform.dev/latex/commands/sec) | command | Used for secant in trigonometric formulas and identities | base, physics | full | full | full | 0.02% |
| [\\varinjlim](https://texform.dev/latex/commands/varinjlim) | command | Typesetting the variable-style direct-limit operator in category theory, algebra, and related areas. | ams | full | full | full | 0.02% |
| [\\csc](https://texform.dev/latex/commands/csc) | command | Used for cosecant in trigonometric identities and specialized calculations | base, physics | full | full | full | 0.02% |
| [\\hom](https://texform.dev/latex/commands/hom) | command | Used for Hom in algebra, category theory, and homological algebra | base | full | full | full | 0.01% |
| [\\varlimsup](https://texform.dev/latex/commands/varlimsup) | command | Producing the variable-style limit superior operator used in analysis notation. | ams | full | full | full | <0.01% |
| [\\lg](https://texform.dev/latex/commands/lg) | command | Used for decimal logarithm notation in some mathematical writing traditions | base | full | full | full | <0.01% |
| [\\varliminf](https://texform.dev/latex/commands/varliminf) | command | Producing the variable-style limit inferior operator used in analysis notation. | ams | full | full | full | <0.01% |
| [\\pod](https://texform.dev/latex/commands/pod) | command | Used to add a parenthesized qualifier such as a modulus or side condition after an expression | base | full | full | none | <0.01% |
| [\\projlim](https://texform.dev/latex/commands/projlim) | command | Used in algebra, topology, and category theory to denote a projective/inverse limit, often with subscripts indicating the indexing system. | ams | full | full | full | <0.01% |
| [\\injlim](https://texform.dev/latex/commands/injlim) | command | Used in category theory, algebra, and homological algebra to denote an injective/direct limit, often with subscripts indicating the indexing system. | ams | full | full | full | <0.01% |
| [\\acosecant](https://texform.dev/latex/commands/acosecant) | command | Alternate physics-package name for the inverse cosecant function using the acsc form | physics | full | none | full | — |
| [\\acosine](https://texform.dev/latex/commands/acosine) | command | Alternate physics-package name for the inverse cosine function using the acos form | physics | full | none | full | — |
| [\\acotangent](https://texform.dev/latex/commands/acotangent) | command | Alternate physics-package name for the inverse cotangent function using the acot form | physics | full | none | full | — |
| [\\arccosecant](https://texform.dev/latex/commands/arccosecant) | command | Alternate physics-package name for the inverse cosecant function | physics | full | none | full | — |
| [\\arccosine](https://texform.dev/latex/commands/arccosine) | command | Alternate physics-package name for the inverse cosine function | physics | full | none | full | — |
| [\\arccotangent](https://texform.dev/latex/commands/arccotangent) | command | Alternate physics-package name for the inverse cotangent function | physics | full | none | full | — |
| [\\arcsecant](https://texform.dev/latex/commands/arcsecant) | command | Alternate physics-package name for the inverse secant function | physics | full | none | full | — |
| [\\arcsine](https://texform.dev/latex/commands/arcsine) | command | Alternate physics-package name for the inverse sine function | physics | full | none | full | — |
| [\\arctangent](https://texform.dev/latex/commands/arctangent) | command | Alternate physics-package name for the inverse tangent function | physics | full | none | full | — |
| [\\asecant](https://texform.dev/latex/commands/asecant) | command | Alternate physics-package name for the inverse secant function using the asec form | physics | full | none | full | — |
| [\\asine](https://texform.dev/latex/commands/asine) | command | Alternate physics-package name for the inverse sine function using the asin form | physics | full | none | full | — |
| [\\atangent](https://texform.dev/latex/commands/atangent) | command | Alternate physics-package name for the inverse tangent function using the atan form | physics | full | none | full | — |
| [\\cosecant](https://texform.dev/latex/commands/cosecant) | command | Alternate physics-package name for the cosecant function in formulas | physics | full | none | full | — |
| [\\cosine](https://texform.dev/latex/commands/cosine) | command | Alternate physics-package name for the cosine function in formulas | physics | full | none | full | — |
| [\\cotangent](https://texform.dev/latex/commands/cotangent) | command | Alternate physics-package name for the cotangent function in formulas | physics | full | none | full | — |
| [\\DeclareMathOperator](https://texform.dev/latex/commands/DeclareMathOperator) | command | Defines a custom named math operator once, so later uses like \foo behave as proper operators (e.g. for custom operators such as argmax, rank, or Res). | ams | full | none | none | — |
| [\\determinant](https://texform.dev/latex/commands/determinant) | command | Alternate physics-package name for the determinant operator | physics | full | none | full | — |
| [\\exponential](https://texform.dev/latex/commands/exponential) | command | Alternate physics-package name for the exponential function operator | physics | full | none | full | — |
| [\\hypcosecant](https://texform.dev/latex/commands/hypcosecant) | command | Alternate physics-package name for the hyperbolic cosecant function | physics | full | none | full | — |
| [\\hypcosine](https://texform.dev/latex/commands/hypcosine) | command | Alternate physics-package name for the hyperbolic cosine function | physics | full | none | full | — |
| [\\hypcotangent](https://texform.dev/latex/commands/hypcotangent) | command | Alternate physics-package name for the hyperbolic cotangent function | physics | full | none | full | — |
| [\\hypsecant](https://texform.dev/latex/commands/hypsecant) | command | Alternate physics-package name for the hyperbolic secant function | physics | full | none | full | — |
| [\\hypsine](https://texform.dev/latex/commands/hypsine) | command | Alternate physics-package name for the hyperbolic sine function | physics | full | none | full | — |
| [\\hyptangent](https://texform.dev/latex/commands/hyptangent) | command | Alternate physics-package name for the hyperbolic tangent function | physics | full | none | full | — |
| [\\logarithm](https://texform.dev/latex/commands/logarithm) | command | Alternate physics-package name for the logarithm operator | physics | full | none | full | — |
| [\\naturallogarithm](https://texform.dev/latex/commands/naturallogarithm) | command | Alternate physics-package name for the natural logarithm operator | physics | full | none | full | — |
| [\\Probability](https://texform.dev/latex/commands/Probability) | command | Alternate physics-package name for the probability operator | physics | full | none | full | — |
| [\\rank](https://texform.dev/latex/commands/rank) | command | Used to denote the rank of a matrix, tensor, or linear map | physics | full | none | full | — |
| [\\secant](https://texform.dev/latex/commands/secant) | command | Alternate physics-package name for the secant function in formulas | physics | full | none | full | — |
| [\\sine](https://texform.dev/latex/commands/sine) | command | Alternate physics-package name for the sine function in formulas | physics | full | none | full | — |
| [\\tangent](https://texform.dev/latex/commands/tangent) | command | Alternate physics-package name for the tangent function in formulas | physics | full | none | full | — |