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The Greek alphabet is used to write the Greek language, and at one point was even used for a numeral system.[1] 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
Alpha
alpha Fine structure constant (A003673)
Beta Euler Beta function
beta
Gamma Euler Gamma function
gamma Euler-Mascheroni constant (A001620)

, the th Stieltjes constant

Delta Nabla (del in vector calculus)

Laplacian or Laplace operator

delta Silver ratio (A014176) Dirac delta function

Kronecker delta function

Wieirstraas epsilon-delta notation
psilon
, epsilon Wieirstraas epsilon-delta notation

Levi-Civita permutation symbol [2]

Zeta
zeta Riemann zeta function (the classic "zeta function")[3]

Dedekind zeta function[4]
Weierstrass zeta function[5]
● Complex th root of unity [6]

Eta
eta
Theta
, theta Chebyshev or Tschebycheff function [7][8] ● Angle symbol
Iota
iota
Kappa
kappa
Lambda Mangoldt lambda function -dimensional lattice [9]
lambda Carmichael lambda function (A002322)[10]

Liouville lambda function (A008836)

Mu
mu ● Madachy's constant (A130701)[11] Möbius function (A008683) Fundamental unit in when [12]
Nu
nu ● Exponent of the highest power of the prime that divides [13]

● Alternate notation for number of distinct prime factors function (also ) (A001221)[14]

Xi
xi
Omicron
omicron
Pi Product operator
, pi Archimedes' constant (A000796) Prime counting function (A000720) gives )

● Euler's original notation for the totient function [15]

Rho
, rho Prime constant (A051006) Digital root function [16] (A010888) Pollard's rho method

th zero of in the upper half of the critical strip[17]

Sigma Summation operator
, sigma Number of divisors function (A000005)

Sum of divisors function
Sum of th powers of divisors function
● The real part of a complex number, by Riemann's notation[18]

Tau
tau ● Alternative symbol for the golden ratio [19] ● Alternative notation for [20][21]

Ramanujan tau function (A000594)

Upsilon
upsilon
Phi Totient summatory function th cyclotomic polynomial [22]

● The Frattini subgroup of a group
● The group of units of [23]

, phi Golden ratio (A001622) Euler's totient function
Chi
chi ● A characteristic function, like the characteristic function of the primes Modular character
Psi
psi ● Alternative notation for the Liouville lambda function

● Alternative notation for the Carmichael reduced totient function
Dedekind psi function

Omega Chaitin's constant Number of prime factors function (A001222)[24] ● The th omega subgroup of a -group

● The th agemo subgroup of a -group

omega ● Smallest countably infinite ordinal number Number of distinct prime factors function [25][26] ● Complex cubic root of unity [27]

See also

Notes

  1. Kühner, p. 121
  2. PlanetMath, Levi-Civita permutation symbol
  3. Dan Rockmore, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers. New York: Pantheon Books (2005) p. 143
  4. Rockmore, ibid.
  5. Weisstein, Eric W. "Weierstrass Zeta Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/WeierstrassZetaFunction.html
  6. Paulo Ribenboim, The New Book of Prime Number Records New York: Springer-Verlag (1996): p. xxi
  7. Or as in Paulo Ribenboim, The New Book of Prime Number Records New York: springer-Verlag (1996): p. xx
  8. The variant is also used. Weisstein, Eric W. "Chebyshev Functions." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ChebyshevFunctions.html
  9. N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences San Diego: Academic Press (1995): p. xii
  10. Paulo Ribenboim, The New Book of Prime Number Records New York: springer-Verlag (1996): p. xviii
  11. Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, New York: Prometheus Books, 2007, page 171.
  12. Ethan D. Bolker, Elementary Number Theory: An Algebraic Approach Mineola, New York: Dover Publications (1969, reprinted 2007): 175
  13. L. Carlitz, "The Highest Power of a Prime Dividing Certain Quotients" Archiv der Mathematik 18 2 (1967) p. 157
  14. In Wolfram Mathematica, this seems to be more about keeping the function PrimeOmega[n] unambiguously reserved for . http://reference.wolfram.com/mathematica/ref/PrimeNu.html
  15. D. N. Lehmer, "Dickson's History of the Theory of Numbers" Bull. Amer. Math. Soc. 26 3 (1919), 128.
  16. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 283, Supplementary Exercises 1 - 3. This is the only place I've seen this meaning assigned to this notation.
  17. Paulo Ribenboim, The New Book of Prime Number Records New York: springer-Verlag (1996): p. xx
  18. Władysław Narkiewicz, The Development of Prime Number Theory: From Euclid to Hardy and Littlewood Berlin: Springer-Verlag (2000): p. xi
  19. As for example, in N. J. A. Sloane & Simon Plouffe, The Encyclopedia of Integer Sequences. San Diego: Academic Press (1995): p. xii
  20. Thomas Koshy, Elementary Number Theory with Applications. Harcourt Academic Press (2002): p. 353, Section 8.2
  21. Or as in Paulo Ribenboim, The New Book of Prime Number Records New York: Springer-Verlag (1996): p. xix
  22. Paulo Ribenboim, The New Book of Prime Number Records New York: Springer-Verlag (1996): p. xxi
  23. Ethan D. Bolker, Elementary Number Theory: An Algebraic Approach Mineola, New York: Dover Publications (1969, reprinted 2007): 175
  24. Manfred R. Schroeder, Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity 5th Ed. Springer (2009) p. 407
  25. As for example, in Paulo Ribenboim, The New Book of Prime Number Records New York: springer-Verlag (1996): p. xvii
  26. Or as in Manfred R. Schroeder, Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity 5th Ed. Springer (2009) p. 407
  27. Manfred R. Schroeder, Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity 5th Ed. Springer (2009) p. 407

References

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