List of q-analogs

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

Algebra

 * Iwahori–Hecke algebra
 * Quantum affine algebra
 * Quantum enveloping algebra
 * Quantum group

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