Latin letters used in mathematics | Wikipedia audio article
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Many letters of the Latin alphabet, both capital
and small, are used in mathematics, science and engineering to denote by convention specific
or abstracted constants, variables of a certain type, units, multipliers, physical entities.
Certain letters, when combined with special formatting, take on special meaning.
Below is an alphabetical list of the letters of the alphabet with some of their uses. The
field in which the convention applies is mathematics unless otherwise noted.==Aa==
A represents: the first point of a triangle
the digit “10” in hexadecimal and other positional numeral systems with a radix of 11 or greater
the unit ampere for electric current in physics the area of a figure
the mass number of an element in chemistry the Helmholtz free energy of a closed thermodynamic
system of constant pressure and temperature a vector potential, in electromagnetics it
can refer to the magnetic vector potential an Abelian group in abstract algebra
the Glaisher–Kinkelin constant 𝔸 ( A {\displaystyle \mathbb {A} }
) represents the algebraic numbers or affine space in algebraic geometry
a represents: the first side of a triangle (opposite point
A) the scale factor of the expanding universe
in cosmology the acceleration in mechanics equations
the x-intercept of a line using the line equation the unit are for area (100 m²)
the unit prefix atto (10−18) the first term in a sequence or series==Bb==
B represents: the digit “11” in hexadecimal and other positional
numeral systems with a radix of 12 or greater the second point of a triangle
a ball (also denoted by ℬ ( B {\displaystyle {\mathcal {B}}}
) or 𝔹 ( B {\displaystyle \mathbb {B} }
)) a basis of a vector space or of a filter (both
also denoted by ℬ ( B {\displaystyle {\mathcal {B}}}
)) in econometrics and time-series statistics
it is often used for the backshift or lag operator, the formal parameter of the lag
polynomial the magnetic field, denoted B {\displaystyle {\textbf {B}}}
or B
→ {\displaystyle {\vec {B}}} B with various subscripts represents several
variations of Brun’s constant and Betti numbers; it can also be used to mean the Bernoulli
numbers b represents:
the second side of a triangle (opposite point B)
The impact parameter in nuclear scattering the y-intercept of a line using the line equation
usually with an index, sometimes with an arrow over it, a basis vector==Cc==
C represents: the third point of a triangle
the digit “12” in hexadecimal and other positional numeral systems with a radix of 13 or greater
the unit coulomb of electrical charge capacitance in electrical theory
with indices denotes the number of combinations, a binomial coefficient
together with a degree symbol (°) represents the Celsius measurement of temperature=°C
the circumference of a circle or other closed curve
C represents: an arbitrary category
ℂ ( C {\displaystyle \mathbb {C} }
) represents the set of complex numbers A vertically elongated C with an integer subscript
n sometimes denotes the n-th coefficient of a formal power series.
c represents: the unit prefix centi (10−2)
the molar concentration in chemistry c represents:
the speed of light in a vacuum the third side of a triangle (opposite corner
C) Lower case Fraktur c {\displaystyle {\mathfrak {c}}}
denotes the cardinality of the set of real numbers (the “continuum”), or, equivalently,
of the power set of natural numbers==Dd==
D represents the digit “13” in hexadecimal and other positional
numeral systems with a radix of 14 or greater diffusion coefficient or diffusivity in dimensions
of [length^2 / time] the differential operator in Euler’s calculus
notation d represents
the differential operator the unit day of time (86,400 s)
the difference in an arithmetic sequence a metric operator/function
the diameter of a circle==Ee==
E represents: the digit “14” in hexadecimal and other positional
numeral systems with a radix of 15 or greater an exponent in decimal numbers. For example,
1.2E3 is 1.2×10³ or 1200 the set of edges in a graph or matroid
the unit prefix exa (1018) energy in physics
electric field denoted E {\displaystyle {\textbf {E}}}
or E
→ {\displaystyle {\vec {E}}} electromotive force (denoted E {\displaystyle {\mathcal {E}}}
and measured in volts), refers to voltage. an event (as in P(E), which reads “the probability
P of event E occurring”) in statistics, the expected value of a random
variable e represents:
Euler’s number, a transcendental number equal to 2.71828182845… which is used as the base
for natural logarithms a vector of unit length, especially in the
direction of one of the coordinates axes the elementary charge in physics
an electron, usually donated e− to distinguish against a positron e+
the eccentricity of a conic section the identity element in a group==Ff==
F represents the digit “15” in hexadecimal and other positional
numeral systems with a radix of 16 or greater the unit farad of electrical capacity
the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature
together with a degree symbol (°) represents the Fahrenheit measurement of temperature
=°F F represents
force in mechanics equations pFq is a hypergeometric series
the probability distribution function in statistics a Fibonacci number
an arbitrary functor f represents:
the unit prefix femto (10−15) f represents:
the generic designation of a function==Gg==
G represents an arbitrary graph, as in: G(V,E)
an arbitrary group the unit prefix giga (109)
Newton’s gravitational constant the Einstein tensor
the Gibbs energy the centroid of a triangle
Catalan’s constant g represents:
the generic designation of a second function the acceleration due to gravity on Earth==Hh==
H represents: a Hilbert space
the unit henry of magnetic inductance the homology and cohomology functors
the (Shannon) entropy of information the orthocenter of a triangle
a partial sum of the harmonic series magnetic field, denoted H {\displaystyle {\boldsymbol {H}}}
. H0 represents Hubble’s parameter as measures
today (100 h km·s−1·Mpc−1 with h being the associated error)
ℍ ( H {\displaystyle \mathbb {H} }
) represents the quaternions (after William Rowan Hamilton)
ℋ ( H {\displaystyle {\mathcal {H}}}
) represents the Hamiltonian in Hamiltonian mechanics
h represents: the class number in algebraic number theory
a small increment in the argument of a function the unit hour for time (3600 s)
the Planck constant (6.626 069(57)× 10−34 J·s)
the unit prefix hecto (102) the altitude of a triangle==Ii==
I represents: the closed unit interval, which contains all
real numbers from 0 to 1, inclusive the identity matrix
the Irradiance the moment of inertia
Intensity in physics the incenter of a triangle
I represents: the index of an indexed family
i represents: the imaginary unit, a complex number that
is the square root of −1 a subscript to denote the ith term (that is,
a general term or index) in a sequence or list
the index to the elements of a vector, written as a subscript after the vector name
the index to the rows of a matrix, written as the first subscript after the matrix name
an index of summation using the sigma notation the unit vector in Cartesian coordinates going
in the X-direction, usual bold i==Jj==
J represents: the unit joule of energy
the current density in electromagnetism denoted J {\displaystyle {\boldsymbol {J}}}
. the Radiosity in thermal mechanics
J represents: the scheme of a diagram in category theory
j represents: the index to the columns of a matrix, written
as the second subscript after the matrix name in electrical engineering, the square root
of −1, instead of i in electrical engineering, the principal cube
root of 1: − 1
2 + 1
2 i 3 {\displaystyle -{\frac {1}{2}}+{\frac {1}{2}}i{\sqrt
{3}}}==Kk==
K represents: the unit kelvin of temperature
the functors of K-theory an unspecified (real) constant
a field in algebra the area of a polygon
k represents the unit prefix kilo- (10³)
the Boltzmann constant, this is often represented as kB to avoid confusion with
the Wavenumber of the wave equation an integer, e.g. a dummy variable in summations,
or an index of a matrix. an unspecified (real) constant
the spring constant of Hooke’s law the spacetime Curvature from the Friedmann
equations in cosmology==Ll==
L represents: Length, used often in quantum mechanics as
the size of an infinite square well Angular momentum
the unit of volume the litre the radiance
the space of all integrable real (or complex) functions
the space of linear maps, as in L(E,F) or L(E)=End(E)
the likelihood function a formal language
the lag operator in statistics a Lucas number
l represents: the unit of volume the litre
the length of a side of a rectangle or a rectangular prism (e.g. V=lwh; A=lw)
the last term of a sequence or series (e.g. Sn=n(a+l)/2)
ℒ ( L {\displaystyle {\mathcal {L}}}
) represents: the Lagrangian (sometimes just L)
Exposure (in particle physics)==Mm==
M represents: a manifold
a metric space a matroid
the unit prefix mega- (106) the Madelung constant for crystal structures
held by ionic bonding m represents:
the number of rows in a matrix the slope in a linear regression or in any
line the mass in mechanics equations
the unit metre of length the unit prefix milli (10−3)
a median of a triangle==Nn==
N represents the unit newton of force
the Neutron number the Particle number in thermodynamics
The number of particles of a thermodynamical system
the nine-point center of a triangle NA represents the Avogadro constant which
is the number of entities in one mole (used mainly in the counting of molecules and atoms)
and is 6.022 141 79(30) × 10,23 mol −1 ℕ ( N {\displaystyle \mathbb {N} }
) represents the natural numbers n represents
the number of columns in a matrix the “number of” in algebraic equations.
A neutron, often shown as 10n the Number density of particles in a Volume
the unit prefix nano (10−9) the nth term of a sequence or series (e.g.
tn=a+(n-1)d) the principal quantum number==Oo==
O represents the order of asymptotic behavior of a function
(upper bound); see Big O notation (
0 ,
0 ,
… ,
0 ) {\displaystyle (0,0,\ldots ,0)}
— the origin of the coordinate system in Cartesian coordinates
the circumcenter of a triangle or other cyclic polygon, or more generally the center of a
circle o represents
the order of asymptotic behavior of a function (strict upper bound); see Little o notation
the order of an element in a group==Pp==
P represents: the pressure in physics equations
the unit prefix peta (1015) probability in statistics and statistical
mechanics an arbitrary point in geometry
ℙ ( P {\displaystyle \mathbb {P} }
) represents the prime numbers
projective space a probability (as in P(E), which reads “the
probability P of event E happening”) p represents
the unit prefix pico (10−12) a proton, often p+ or 11 p
the linear momentum in physics equations the perimeter of a triangle or other polygon==Qq==
Q represents: heat energy
ℚ ( Q {\displaystyle \mathbb {Q} }
) represents the rational numbers q represents:
the deceleration parameter in cosmology electric charge of a particle==Rr==
R represents: the Ricci tensor
the circumradius of a cyclic polygon such as a triangle
an arbitrary relation ℝ ( R {\displaystyle \mathbb {R} }
) represents the set of real numbers and various algebraic structures built upon the set of
real numbers, such as R n {\displaystyle \mathbb {R} ^{n}} r represents:
the radius of a circle or sphere the inradius of a triangle or other tangential
polygon the ratio of a geometric series (e.g. arn-1)
the separation of two objects, for example in Coulomb’s law==Ss==
S represents a sum
the unit siemens of electric conductance the unit sphere (with superscript denoting
dimension) the scattering matrix
entropy s represents:
an arclength the displacement in mechanics equations
the unit second of time a complex variable s=σ + i t in analytic
number theory the semiperimeter of a triangle or other polygon
𝒮 ( S {\displaystyle {\mathcal {S}}}
) represents a system’s action in physics==Tt==
T represents: the top element of a lattice
a tree (a special kind of graph) temperature in physics equations
the unit tesla of magnetic flux density the unit prefix tera (1012)
the stress–energy tensor tension in physics
an arbitrary monad t represents:
time in graphs, functions or equations a term in a sequence or series (e.g. tn=tn−1+5)
the imaginary part of the complex variable s=σ + i t in analytic number theory
the sample statistic resulting from a Student’s t-test==Uu==
U represents: a U-set which is a set of uniqueness
a unitary operator in thermodynamics, the internal energy of
a system a forgetful functor
U(n) represents the unitary group of degree n
∪ represents the union operator==Vv==
V represents: volume
the unit volt of voltage the set of vertices in a graph
a vector space v represents the velocity in mechanics equations==Ww==
W represents: the unit watt of power
work, both mechanical & thermodynamical in thermodynamics, the number of possible
quantum states in Boltzmann’s entropy formula w represents:
the coordinate on the fourth axis in four-dimensional space.==Xx==
X represents a random variable
a triangle center x represents
a realized value of a random variable an unknown variable, most often (but not always)
from the set of real numbers, while a complex unknown would rather be called z, and an integer
by a letter like m from the middle of the alphabet.
the coordinate on the first or horizontal axis in a Cartesian coordinate system, or
the viewport in a graph or window in computer graphics.==Yy==
Y represents: the unit prefix yotta- (1024)
Y represents: a second random variable
y represents: the unit prefix yocto- (10−24)
y represents: a realized value of a second random variable
a second unknown variable the coordinate on the second or vertical axis
(backward axis in three dimensions) in a linear coordinate system, or in the viewport of a
graph or window in computer graphics.==Zz==
Z represents: the unit prefix zetta (1021)
the atomic number in chemistry and physics a standardized normal random variable in probability
theory and statistics The partition function in statistical mechanics
in meteorology, the radar reflectivity factor ℤ ( Z {\displaystyle \mathbb {Z} }
) represents the integers z represents:
the unit prefix zepto (10−21) the coordinate on the third or vertical axis
in three dimensional space the view depth in computer graphics, see also
“z-buffering” the argument of a complex function, or any
other variable used to represent a complex value
in astronomy, wavelength redshift a third unknown variable==See also==
Blackboard bold letters used in mathematics Greek letters used in mathematics
List of letters used in mathematics and science Mathematical alphanumeric symbols
Table of mathematical symbols Typographical conventions in mathematical
formulae

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