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