Greek letters used in mathematics

From Freepedia

Greek letters are used in mathematics, science, and engineering 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. Sometimes font variants of Greek letters are used as distinct symbols in mathematics.

Αα (Alpha)

• α represents the first angle in a triangle, opposite the side A.

Ββ (Beta)

• B represents the Beta function.
• β represents the second angle in a triangle, opposite the side B.

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
• γ represents:
  • the third angle in a triangle, opposite the side C [sic]
  • the Euler-Mascheroni constant in mathematics.
  • a risk management measure in mathematical finance.

Δδ (Delta)

• Δ represents a finite difference or difference operator, like Δ or Δx.
• δ represents:
  • a variation in the calculus of variations
  • the Kronecker delta function
  • the Dirac delta function

Εε (Epsilon)

• ε represents:
  • a small positive infinitesimal quantity.
  • in set theory, the limit ordinal of the sequence <math>\omega,\omega^{\omega},\omega^{\omega^{\omega}},\dots</math>.
  • in computer science, the empty string.
  • the Levi-Civita symbol.
  • set membership (often written ∈ instead of ε), especially in older texts.

Ζζ (Zeta)

• ζ represents:
  • the Riemann zeta function and other zeta functions in mathematics
  • the coefficient of viscous friction in polymer dynamics

Ηη (Eta)

• η represents the partial regression coefficient in statistics.

Θθ (Theta)

• Θ represents an asymptotically tight bound related to Big O notation.
• θ represents:
  • a plane angle in geometry
  • the angle to the x axis in the xy-plane in spherical or cylindrical coordinates

Ιι (Iota)

Κκ (Kappa)

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

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.

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

Νν (Nu)

• ν represents:
  • frequency in physics

Ξξ (Xi)

• ξ represents a random variable.

Οο (Omicron)

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

Ππ (Pi)

• Π is the product operator in mathematics.
• π represents:
  • the ratio of a circle's circumference to its diameter
  • the prime counting function

Ρρ (Rho)

• ρ represents:
  • the radius in a polar coordinate system
  • the correlation coefficient in statistics

Σσ (Sigma)

• Σ is the summation operator.
• σ sigma represents the divisor function in number theory and the population standard deviation or spread in probability and statistics.

Ττ (Tau)

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

Υυ (Upsilon)

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

Χχ (Chi)

• χ represents:
  • the chi-square distribution in statistics
  • the chromatic number of a graph in graph theory
  • the Euler characteristic in algebraic topology

Ψψ (Psi)

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

Ωω (Omega)

• Ω represents:
  • the Omega constant
  • an asymptotic lower bound related to Big O notation
  • in probability theory, the set of possible outcomes of an experiment
• ω represents:
  • the first infinite ordinal
  • an asymptotically dominant quantity related to Big O notation
  • in probability theory, a possible outcome of an experiment

See also

• Greek alphabet
• Roman letters used in mathematics
• Mathematical alphanumeric symbols
• Table of mathematical symbols
• Typographical conventions in mathematical formulae