Category

Q-analogs

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Stirling number

important functions in combinatorics

q-Pochhammer symbol

q-analog of the Pochhammer symbol

Ramanujan theta function

mathematic term

mathematical term

In mathematics, a '''q-analog' of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as . Typically, mathematicians are interested in q-analogs that arise naturally, rather than in arbitrarily contriving q-analogs of known results. The earliest q''-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century.

the mathematical function ∏ₖ₌₁^∞ (1−𝑞ᵏ)

German mathematician (1911-1998)

Gaussian binomial coefficient

family of polynomials

Rogers–Ramanujan identities

Mathematical identities related to basic hypergeometric series

In mathematics, in the area of combinatorics and quantum calculus, the '''q-derivative, or Jackson derivative', is a q''-analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's q-integration. For other forms of q-derivative, see .

Elliptic gamma function

Elliptic analog of the gamma function

basic hypergeometric series

q-analog of hypergeometric series

mock modular form

complex-differentiable part of a Maass wave function

Q-theta function

q-gamma function

q-analog of the gamma function

The term '''q-exponential''' occurs in two contexts. The q-exponential distribution, based on the Tsallis q-exponential is discussed in elsewhere.

Askey–Wilson polynomials

family of orthogonal polynomials made by Askey & Wilson as q-analogs of Wilson polynomials

Rogers–Ramanujan continued fraction

Continued fraction closely related to the Rogers–Ramanujan identities

Rogers polynomials

Family of orthogonal polynomials

Rogers–Szegő polynomials

family of polynomials orthogonal on the unit circle introduced by Szegő (1926)