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- Q-analog abstract "Roughly speaking, in mathematics, specifically in the areas of combinatorics and special functions, 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 q → 1. Typically, mathematicians are interested in q-analogues that arise naturally, rather than in arbitrarily contriving q-analogues of known results. The earliest q-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century.q-analogs find applications in a number of areas, including the study of fractals and multi-fractal measures, and expressions for the entropy of chaotic dynamical systems. The relationship to fractals and dynamical systems results from the fact that many fractal patterns have the symmetries of Fuchsian groups in general (see, for example Indra's pearls and the Apollonian gasket) and the modular group in particular. The connection passes through hyperbolic geometry and ergodic theory, where the elliptic integrals and modular forms play a prominent role; the q-series themselves are closely related to elliptic integrals.q-analogs also appear in the study of quantum groups and in q-deformed superalgebras. The connection here is similar, in that much of string theory is set in the language of Riemann surfaces, resulting in connections to elliptic curves, which in turn relate to q-series.There are two main groups of q-analogs, the "classical" q-analogs, with beginnings in the work of Leonhard Euler and extended by F. H. Jackson and others.".
- Q-analog wikiPageExternalLink q-Analog.html.
- Q-analog wikiPageExternalLink q-BinomialCoefficient.html.
- Q-analog wikiPageExternalLink q-Bracket.html.
- Q-analog wikiPageExternalLink q-Factorial.html.
- Q-analog wikiPageID "1619396".
- Q-analog wikiPageLength "7014".
- Q-analog wikiPageOutDegree "50".
- Q-analog wikiPageRevisionID "680630087".
- Q-analog wikiPageWikiLink Algebraic_group.
- Q-analog wikiPageWikiLink Apollonian_gasket.
- Q-analog wikiPageWikiLink Basic_hypergeometric_series.
- Q-analog wikiPageWikiLink Category:Combinatorics.
- Q-analog wikiPageWikiLink Category:Q-analogs.
- Q-analog wikiPageWikiLink Combinatorics.
- Q-analog wikiPageWikiLink Dynamical_system.
- Q-analog wikiPageWikiLink Elliptic_curve.
- Q-analog wikiPageWikiLink Elliptic_integral.
- Q-analog wikiPageWikiLink Entropy.
- Q-analog wikiPageWikiLink Ergodic_theory.
- Q-analog wikiPageWikiLink F._H._Jackson.
- Q-analog wikiPageWikiLink Factorial.
- Q-analog wikiPageWikiLink Field_with_one_element.
- Q-analog wikiPageWikiLink Finite_field.
- Q-analog wikiPageWikiLink Fractal.
- Q-analog wikiPageWikiLink Frank_Hilton_Jackson.
- Q-analog wikiPageWikiLink Fuchsian_group.
- Q-analog wikiPageWikiLink Gaussian_binomial_coefficient.
- Q-analog wikiPageWikiLink Hyperbolic_geometry.
- Q-analog wikiPageWikiLink Indras_Pearls_(book).
- Q-analog wikiPageWikiLink Inversion_(discrete_mathematics).
- Q-analog wikiPageWikiLink Leonhard_Euler.
- Q-analog wikiPageWikiLink Limit_(mathematics).
- Q-analog wikiPageWikiLink List_of_q-analogs.
- Q-analog wikiPageWikiLink MathWorld.
- Q-analog wikiPageWikiLink Mathematics.
- Q-analog wikiPageWikiLink Modular_form.
- Q-analog wikiPageWikiLink Modular_group.
- Q-analog wikiPageWikiLink Multi-fractal_measure.
- Q-analog wikiPageWikiLink Permutation.
- Q-analog wikiPageWikiLink Prime_number.
- Q-analog wikiPageWikiLink Q-Pochhammer_symbol.
- Q-analog wikiPageWikiLink Q-exponential.
- Q-analog wikiPageWikiLink Q-factorial.
- Q-analog wikiPageWikiLink Q-series.
- Q-analog wikiPageWikiLink Quantum_group.
- Q-analog wikiPageWikiLink Ramsey_theory.
- Q-analog wikiPageWikiLink Riemann_surface.
- Q-analog wikiPageWikiLink Special_function.
- Q-analog wikiPageWikiLink Special_functions.
- Q-analog wikiPageWikiLink Sperners_theorem.
- Q-analog wikiPageWikiLink Stirling_number.
- Q-analog wikiPageWikiLink String_theory.
- Q-analog wikiPageWikiLink Superalgebra.
- Q-analog wikiPageWikiLink Vector_space.
- Q-analog wikiPageWikiLink Weyl_group.
- Q-analog wikiPageWikiLink Young_tableau.
- Q-analog wikiPageWikiLinkText "''q'' factorial".
- Q-analog wikiPageWikiLinkText "''q'' number".
- Q-analog wikiPageWikiLinkText "''q''-analog".
- Q-analog wikiPageWikiLinkText "''q''-analogs".
- Q-analog wikiPageWikiLinkText "''q''-analogue".
- Q-analog wikiPageWikiLinkText "''q''-analogues".
- Q-analog wikiPageWikiLinkText "Q-analog".
- Q-analog wikiPageWikiLinkText "q-analog".
- Q-analog wikiPageWikiLinkText "q-digamma".
- Q-analog wikiPageWikiLinkText "q-mapping".
- Q-analog hasPhotoCollection Q-analog.
- Q-analog id "/U/u095050".
- Q-analog title "Umbral calculus".
- Q-analog wikiPageUsesTemplate Template:Main.
- Q-analog wikiPageUsesTemplate Template:Springer.
- Q-analog subject Category:Combinatorics.
- Q-analog subject Category:Q-analogs.
- Q-analog hypernym Generalization.
- Q-analog type Combinatoric.
- Q-analog type Field.
- Q-analog type Function.
- Q-analog comment "Roughly speaking, in mathematics, specifically in the areas of combinatorics and special functions, 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 q → 1. Typically, mathematicians are interested in q-analogues that arise naturally, rather than in arbitrarily contriving q-analogues of known results.".
- Q-analog label "Q-analog".
- Q-analog sameAs Q-analogia.
- Q-analog sameAs Q-analogue.
- Q-analog sameAs Q-類似.
- Q-analog sameAs Q-analog.
- Q-analog sameAs m.05h65n.
- Q-analog sameAs Q3491352.
- Q-analog sameAs Q3491352.
- Q-analog sameAs Q-模拟.
- Q-analog wasDerivedFrom Q-analog?oldid=680630087.
- Q-analog isPrimaryTopicOf Q-analog.