List of q-analogs

This is a list of q-analogs in mathematics and related fields.

Algebra

Analysis

  • Jackson integral
  • q-derivative
  • q-difference polynomial
  • Quantum calculus

Combinatorics

  • LLT polynomial
  • q-binomial coefficient
  • q-Pochhammer symbol
  • q-Vandermonde identity

Orthogonal polynomials

  • q-Bessel polynomials
  • q-Charlier polynomials
  • q-Hahn polynomials
  • q-Jacobi polynomials:
    • Big q-Jacobi polynomials
    • Continuous q-Jacobi polynomials
    • Little q-Jacobi polynomials
  • q-Krawtchouk polynomials
  • q-Laguerre polynomials
  • q-Meixner polynomials
  • q-Meixner–Pollaczek polynomials
  • q-Racah polynomials

Probability and statistics

  • Gaussian q-distribution
  • q-exponential distribution
  • q-Weibull diribution
  • Tsallis q-Gaussian
  • Tsallis entropy

Special functions

  • Basic hypergeometric series
  • Elliptic gamma function
  • Hahn–Exton q-Bessel function
  • Jackson q-Bessel function
  • q-exponential
  • q-gamma function
  • q-theta function

See also