q-Analog

A -analog, also called a q-Extension or q-Generalization, is a mathematical expression parameterized by a quantity which generalizes a known expressionand reduces to the known expression in the limit . There are -analogs of the Factorial,Binomial Coefficient, Derivative, Integral, Fibonacci Numbers, andso on. Koornwinder, Suslov, and Bustoz, have even managed some kind of -Fourier analysis.

The -analog of a mathematical object is generally called the ``-object'', hence q-Binomial Coefficient, q-Factorial, etc. There are generally several-analogs if there is one, and there is sometimes even a multibasic analog with independent , , ....

References

Exton, H. -Hypergeometric Functions and Applications. New York: Halstead Press, 1983.

• Pohlke's Theorem
• Poincaré-Birkhoff Fixed Point Theorem
• Poincaré Conjecture
• Poincaré Duality
• Poincaré Formula
• Poincaré-Fuchs-Klein Automorphic Function
• Poincaré Group
• Poincaré-Hopf Index Theorem
• Poincaré Hyperbolic Disk
• Poincaré Manifold
• Poincaré Metric
• Poincaré Separation Theorem
• Poincaré's Holomorphic Lemma
• Poincaré's Lemma
• Poinsot Solid
• Poinsot's Spirals
• Point
• Point at Infinity
• Point Estimator
• Point Groups
• Point-Line Distance--2-D
• Point-Line Distance--3-D
• Point Picking
• Point-Plane Distance
• Point-Point Distance--1-D