Search results for "Elementary function"

showing 3 items of 3 documents

Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

2019

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

Pure mathematicsAlgebra and Number TheorySeries (mathematics)Applied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsNumerical Analysis (math.NA)Type (model theory)33C05 33C90 33E30 41A3601 natural sciencesSecond order moments010101 applied mathematicsComputational MathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsElementary functionHigher order momentsGeometry and TopologyMathematics - Numerical Analysis0101 mathematicsHypergeometric functionAnalysisMathematics
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Shock-capturing schemes: high accuracy versus total-variation boundedness

2007

In this reseach work we analyze the total variation growth of some high order accurate reconstruction procedures used for the design of shock capturing schemes. This study allows to measure how oscillatory a high order accurate method is in terms of the basic elementary function chosen to increase the order of accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Work (thermodynamics)CalculusElementary functionOrder of accuracyApplied mathematicsVariation (game tree)High orderMeasure (mathematics)Shock (mechanics)MathematicsPAMM
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Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions

2011

We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schr\"odinger equations.

Statistics and ProbabilityBreatherMathematics::Analysis of PDEsGeneral Physics and AstronomyFOS: Physical sciences01 natural sciences010305 fluids & plasmasSchrödinger equationsymbols.namesakeMathematics - Analysis of PDEsSimple (abstract algebra)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesFOS: MathematicsElementary function[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematical physicsPhysics[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Statistical and Nonlinear PhysicsLimitingMathematical Physics (math-ph)Mathematics::Spectral TheoryNonlinear systemNonlinear Sciences::Exactly Solvable and Integrable SystemsModeling and SimulationsymbolsAnalysis of PDEs (math.AP)
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