Greek letters used in mathematics

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Greek alphabet Α α Alpha Β β Beta Γ γ Gamma Δ δ Delta Ε ε Epsilon Ζ ζ Zeta Η η Eta Θ θ Theta Ι ι Iota Κ κ Kappa Λ λ Lambda Μ μ Mu Ν ν Nu Ξ ξ Xi Ο ο Omicron Π π Pi Ρ ρ Rho Σ σ Sigma Τ τ Tau Υ υ Upsilon Φ φ Phi Χ χ Chi Ψ ψ Psi Ω ω Omega obsolete letters Ϝ ϝ Digamma San Ϙ ϙ Qoppa Ϡ ϡ Sampi

Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are usually not used: capital A, B, E, H, I, K, M, N, O, P, T, X, Y, Z; small o. Small ι (iota) and υ (upsilon) are also rarely used, since they closely resemble the Latin letters i and u. Sometimes font variants of Greek letters are used as distinct symbols in mathematics.

In mathematical finance, The Greeks are the variables denoted by Greek letters used to describe the risk of certain investments.

English-speaking mathematicians use neither the modern nor the historical Greek pronunciations of the names of the letters, but the traditional English names, e.g. [ˈθeɪtʌ] for θ cf. ancient [tʰɛ̂ːta] and modern [ˈθita].

[edit] Typography

The Greek letterforms used in mathematics are often different from those used in Greek-language text: they are designed to be used in isolation, not connected to other letters, and some use variant forms which are not normally used in current Greek typography.

The OpenType font format has the feature tag 'mgrk' "Mathematical Greek" to identify a glyph as representing a Greek letter to be used in mathematical (as opposed to Greek language) contexts.

[edit] Αα (Alpha)

• α represents:
  • the first angle in a triangle, opposite the side A.
  • one root of a quadratic equation, where β represents the other
  • the statistical significance of a result
  • the false positive rate in statistics
  • the fine structure constant in Physics
  • the reciprocal of the sacrifice ratio
  • the angle of attack of an airplane

[edit] Ββ (Beta)

• B represents the Beta function.
• β represents:
  • the second angle in a triangle, opposite the side B.
  • one root of a quadratic equation, where α represents the other
  • the ratio of collector current to base current in a bipolar junction transistor (BJT) in electronics
  • the false negative rate in statistics
  • the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance
  • the sideslip angle of an airplane

[edit] Γγ (Gamma)

• Γ represents:
  • the gamma function, a generalization of the factorial
  • the incomplete gamma function
  • the gamma distribution, a continuous probability distribution defined using the gamma function
  • the Christoffel symbols of the second kind
• γ represents:
  • the third angle in a triangle, opposite the side C
  • the Euler-Mascheroni constant in mathematics.
  • second-order sensitivity to price in mathematical finance
  • the ratio of specific heats in thermodynamics.
  • the wavelength within the electromagnetic spectrum
  • used to calculate time and length intervals in special relativity

[edit] Δδ (Delta)

• Δ represents:
  • a finite difference
  • a difference operator
  • the Laplace operator
• δ represents:
  • a variation in the calculus of variations
  • the Kronecker delta function
  • the Dirac delta function
  • sensitivity to price in mathematical finance

[edit] Εε (Epsilon)

• ε represents:
  • a small positive quantity; see limit
  • a random error in regression analysis
  • in set theory, the limit ordinal of the sequence .
  • in computer science, the empty string.
  • the Levi-Civita symbol.
  • in electromagnetics, dielectric permittivity.
• set membership symbol ∈ is based on ε

[edit] Ϝ (Digamma)

• Ϝ is sometimes used to represent the Digamma function, though the Latin letter F (which is nearly identical) is normally substituted.

[edit] Ζζ (Zeta)

• ζ represents:
  • the Riemann zeta function and other zeta functions in mathematics
  • the coefficient of viscous friction in polymer dynamics
  • the damping coefficient for underdamped second-order, linear time-invariant dynamical systems

[edit] Ηη (Eta)

• η represents the partial regression coefficient in statistics.
• η represents elasticities in economicss.

[edit] Θθ (Theta)

• Θ represents:
  • an asymptotically tight bound related to Big O notation.
  • sensitivity to the passage of time in mathematical finance
• θ represents:
  • a plane angle in geometry
  • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates
  • the mean time between failure in reliability engineering
  • soil water contents in soil science

[edit] Ιι (Iota)

[edit] Κκ (Kappa)

• κ represents:
  • the kappa curve
  • the condition number of a matrix in numerical analysis
  • curvature

[edit] Λλ (Lambda)

• Λ represents
  • the set of logical axioms in the axiomatic method of logical deduction in first-order logic
  • the cosmological constant
• λ represents
  • a unit of measure of volume equal to one microlitre (1 μL) or one cubic millimetre (1 mm³).
  • function expressions in the lambda calculus.
  • a general eigenvalue in linear algebra.
  • one wavelength in electromagnetic radiation, esp radio.
  • the arrival rate in queueing theory
  • the average life time or rate parameter in an exponential distribution (commonly used across statistics, physics, and engineering)
  • the failure rate in reliability engineering
  • the expected number of occurrences in a Poisson distribution in probability
  • the lagrange multiplier in the mathematical optimization method, known as the shadow price in economics
  • represents wavelength

[edit] Μμ (Mu)

• μ represents:
  • the Möbius function in number theory
  • the population mean or expected value in probability and statistics
  • a measure in measure theory
  • micro, an SI prefix denoting 10^-6 (one millionth)
  • the coefficient of friction in physics
  • the service rate in queueing theory
  • the dynamic viscosity in physics
  • magnetic permeability in electromagnetics

[edit] Νν (Nu)

• ν represents:
  • frequency in physics
  • Poisson's ratio

[edit] Ξξ (Xi)

• ξ represents a random variable.
• ξ is often used to represent the extent of a chemical reaction.
• Ξ represents the grand canonical ensemble found in statistical mechanics.

[edit] Οο (Omicron)

• The big O notation apparently uses a capital Omicron, not a capital O.

[edit] Ππ (Pi)

• Π is the product operator in mathematics.
• π represents:
  • Archimedes' constant, the ratio of a circle's circumference to its diameter
  • the prime counting function
  • profit in microeconomics and game theory
  • inflation in macroeconomics, expressed as a constant with respects to time
  • the state distribution of a Markov chain
  • a type of covalent bond in Chemistry (Pi bond)

[edit] Ρρ (Rho)

• ρ represents:
  • the radius in a polar coordinate system
  • the correlation coefficient in statistics
  • the sensitivity to interest rate in mathematical finance
  • the density in physics

[edit] Σσ (Sigma)

• Σ is the summation operator.
• σ sigma represents:
  • the divisor function in number theory
  • the population standard deviation or spread in probability and statistics
  • a type of covalent bond in Chemistry (sigma bond)
  • the selection operator in Relational_algebra

[edit] Ττ (Tau)

• τ represents:
  • a correlation coefficient — see Kendall's tau
  • a (small) interval of time

[edit] Υυ (Upsilon)

[edit] Φφ (Phi)

• φ represents:
  • the golden ratio 1.618... in mathematics, art, and architecture
  • Euler's totient function in number theory
  • the argument of a complex number in mathematics
  • the value of a plane angle in physics and mathematics
  • the angle to the z axis in spherical coordinates

[edit] Χχ (Chi)

• χ represents:
  • the chi distribution in statistics (X² is the more frequently encountered chi-square distribution)
  • the chromatic number of a graph in graph theory
  • the Euler characteristic in algebraic topology
  • commonly used as a variable in algebraic equations
  • electronegativity in the periodic table

[edit] Ψψ (Psi)

• ψ represents the wavefunction in the Schrödinger equation of quantum mechanics.

[edit] Ωω (Omega)

• Ω represents:
  • the Omega constant
  • an asymptotic lower bound related to Big O notation
  • in probability theory and statistical mechanics, the set of possible distinct system states
  • the SI unit measure of electric resistance, the ohm
• ω represents:
  • the first infinite ordinal
  • an asymptotically dominant quantity related to Big O notation
  • in probability theory, a possible outcome of an experiment
  • angular velocity / radian frequency
  • a complex cube root of unity - the other is ω²

[edit] See also

• Greek alphabet
• Roman letters used in mathematics
• Mathematical alphanumeric symbols
• Table of mathematical symbols
• Typographical conventions in mathematical formulae
• Greek letters used in physics
• The Greeks (Greek letters used in mathematical finance)