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...

q-analogs in mathematics and related fields. Iwahori–Hecke algebra Quantum affine algebra Quantum enveloping algebra Quantum group Jackson integral q-derivative...

q-analog of the factorial, the q-factorial, as [ n ] ! q = ∏ k = 1 n [ k ] q = [ 1 ] q ⋅ [ 2 ] q ⋯ [ n − 1 ] q ⋅ [ n ] q = 1 − q 1 − q 1 − q 2 1 − q ⋯...

types of calculus in quantum calculus are q-calculus and h-calculus. The goal of both types is to find "analogs" of mathematical objects, where, after taking...

In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone...

polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as ( n k ) q {\displaystyle...

mathematics, a q-exponential is a q-analog of the exponential function, namely the eigenfunction of a q-derivative. There are many q-derivatives, for...

In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general...

several confluent forms of the equation, as shown in the table below. The q-analog of Heun's equation has been discovered by Hahn (1971) and studied by Takemura...

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...