Greek alphabet

The Greek alphabet is used to write the Greek language, and at one point was even used for a numeral system. Mathematicians the world over, however, use certain letters of the Greek alphabet as mathematical symbols.

The Greek alphabet and its usage for mathematical symbols

Letter	Name	Constants	Functions	Miscellaneous
$\mathrm {A} \,$	Alpha
$\alpha \,$	alpha	● Fine structure constant $\scriptstyle \alpha \,\approx \,0.007297\,$ (A003673)
$\mathrm {B} \,$	Beta		● Euler Beta function $\scriptstyle \mathrm {B} (p,q),\,(p,q)\,\in \,\mathbb {C} ^{2}\,$
$\beta \,$	beta
$\Gamma \,$	Gamma		● Euler Gamma function $\scriptstyle \Gamma (z),\,z\,\in \,\mathbb {C} \,$
$\gamma \,$	gamma	● Euler-Mascheroni constant $\scriptstyle \gamma \,\approx \,0.5772\,$ (A001620) ● $\scriptstyle \gamma _{n}\,$, the $\scriptstyle n\,$th Stieltjes constant
$\Delta \,$	Delta			● Nabla $\scriptstyle \nabla \,$ (del in vector calculus) ● Laplacian or Laplace operator $\scriptstyle \Delta \,\equiv \,\nabla ^{2}\,$
$\delta \,$	delta	● Silver ratio $\scriptstyle \delta \,=\,1+{\sqrt {2}}\,\approx \,2.4142\,$ (A014176)	● Dirac delta function $\scriptstyle \delta (x)\,$ ● Kronecker delta function $\scriptstyle \delta _{ij}\,$	● Wieirstraas epsilon-delta notation $\scriptstyle \delta \,$
$\mathrm {E} \,$	psilon
$\epsilon \,$, $\varepsilon \,$	epsilon			● Wieirstraas epsilon-delta notation $\scriptstyle \epsilon \,$ ● Levi-Civita permutation symbol $\scriptstyle \epsilon _{ijk}\,$
$\mathrm {Z} \,$	Zeta
$\zeta \,$	zeta		● Riemann zeta function $\scriptstyle \zeta (z),\,z\,\in \,\mathbb {C} \,$ (the classic "zeta function") ● Dedekind zeta function ● Weierstrass zeta function ● Complex $\scriptstyle n\,$th root of unity $\scriptstyle \zeta _{n}\,=\,\cos {\frac {2\pi }{n}}+i\sin {\frac {2\pi }{n}}\,$
$\mathrm {H} \,$	Eta
$\eta \,$	eta
$\Theta \,$	Theta
$\theta \,$, $\vartheta \,$	theta		● Chebyshev or Tschebycheff function $\scriptstyle \theta (x)\,=\,\sum _{i=1}^{\pi (x)}\log p_{i}\,$	● Angle symbol $\scriptstyle \theta \,$
$\mathrm {I} \,$	Iota
$\iota \,$	iota
$\mathrm {K} \,$	Kappa
$\kappa \,$	kappa
$\Lambda \,$	Lambda		● Mangoldt lambda function $\scriptstyle \Lambda (n)\,$	● $\scriptstyle n\,$-dimensional lattice $\scriptstyle \Lambda _{n}\,$
$\lambda \,$	lambda		● Carmichael lambda function $\scriptstyle \lambda (n)\,$ (A002322) ● Liouville lambda function $\scriptstyle \lambda (n)\,$ (A008836)
$\mathrm {M} \,$	Mu
$\mu \,$	mu	● Madachy's constant $\scriptstyle \mu \,\approx \,1.39418655\,$ (A130701)	● Möbius function $\scriptstyle \mu (n)\,$ (A008683)	● Fundamental unit in $\scriptstyle \mathbb {A} (m)\,$ when $\scriptstyle m\,>\,0\,$
$\mathrm {N} \,$	Nu
$\nu \,$	nu		● Exponent $\scriptstyle \nu (n)\,$ of the highest power of the prime $\scriptstyle p\,$ that divides $\scriptstyle n\,$ ● Alternate notation for number of distinct prime factors function $\scriptstyle \nu (n)\,$ (also $\scriptstyle \omega (n)\,$) (A001221)
$\Xi \,$	Xi
$\xi \,$	xi
$\mathrm {O} \,$	Omicron
$\mathrm {o} \,$	omicron
$\Pi \,$	Pi			● Product operator
$\pi \,$, $\varpi \,$	pi	● Archimedes' constant $\scriptstyle \pi \,\approx \,3.1416\,$ (A000796)	● Prime counting function $\scriptstyle \pi (x)\,$ (A000720) gives $\scriptstyle \pi (n)\,$) ● Euler's original notation $\scriptstyle \pi (n)\,$ for the totient function $\scriptstyle \varphi (n)\,$
$\mathrm {P} \,$	Rho
$\rho \,$, $\varrho \,$	rho	● Prime constant $\scriptstyle \rho \,\approx \,0.4146\,$ (A051006)	● Digital root function $\scriptstyle \rho (n)\,$ (A010888)	● Pollard's rho method ● $\scriptstyle n\,$th zero of $\scriptstyle \zeta (s)\,$ in the upper half of the critical strip
$\Sigma \,$	Sigma			● Summation operator
$\sigma \,$, $\varsigma \,$	sigma		● Number of divisors function $\scriptstyle \sigma (n)\,=\,\sigma _{0}(n)\,$ (A000005) ● Sum of divisors function $\scriptstyle \sigma _{1}(n)\,$ ● Sum of $\scriptstyle k\,$th powers of divisors function $\scriptstyle \sigma _{k}(n)\,$ ● The real part of a complex number, by Riemann's notation
$\mathrm {T} \,$	Tau
$\tau \,$	tau	● Alternative symbol $\scriptstyle \tau \,$ for the golden ratio $\scriptstyle \phi \,$	● Alternative notation $\scriptstyle \tau (n)\,$ for $\scriptstyle \sigma _{0}(n)\,$ ● Ramanujan tau function $\scriptstyle \tau (n)\,$ (A000594)
$\Upsilon \,$	Upsilon
$\upsilon \,$	upsilon
$\Phi \,$	Phi		● Totient summatory function $\scriptstyle \Phi (n)\,$	● $\scriptstyle n\,$th cyclotomic polynomial $\scriptstyle \Phi _{n}(X)\,$ ● The Frattini subgroup $\scriptstyle \Phi (G)\,$ of a group $\scriptstyle G\,$ ● The group of units of $\scriptstyle \mathbb {Z} _{n}\,$
$\phi \,$, $\varphi \,$	phi	● Golden ratio $\scriptstyle \phi \,=\,{\tfrac {1+{\sqrt {5}}}{2}}\,\approx \,1.6180\,$ (A001622)	● Euler's totient function $\scriptstyle \varphi (n)\,$
$\mathrm {X} \,$	Chi
$\chi \,$	chi		● A characteristic function, like the characteristic function of the primes $\chi _{p}(n)$	● Modular character
$\Psi \,$	Psi
$\psi \,$	psi		● Alternative notation $\scriptstyle \psi (n)\,$ for the Liouville lambda function $\scriptstyle \lambda (n)\,$ ● Alternative notation $\scriptstyle \psi (n)\,$ for the Carmichael reduced totient function $\scriptstyle \lambda (n)\,$ ● Dedekind psi function $\scriptstyle \psi (n)\,$
$\Omega \,$	Omega	● Chaitin's constant $\scriptstyle \Omega \,$	● Number of prime factors function $\scriptstyle \Omega (n)\,$ (A001222)	● The $\scriptstyle i\,$th omega subgroup $\scriptstyle \Omega _{i}(G)\,$ of a $\scriptstyle p\,$-group $\scriptstyle G\,$ ● The $\scriptstyle i\,$th agemo subgroup $\scriptstyle \mho ^{i}(G)\,$ of a $\scriptstyle p\,$-group $\scriptstyle G\,$
$\omega \,$	omega	● Smallest countably infinite ordinal number $\scriptstyle \omega \,$	● Number of distinct prime factors function $\scriptstyle \omega (n)\,$	● Complex cubic root of unity $\scriptstyle \omega \,\equiv \,\zeta _{3}\,$

See also

• {{Greek}} (typing-aid template) (Greek letters either as glyphs for HTML or as LaTeX code)
• Latin alphabet
• Greek numerals

References

• R. Kühner, Grammar of the Greek Language, for the Use of High Schools and Colleges. Andover: Allen, Morrill and Wardwell (1844) p. 15