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Mathieu function

In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation

Applications, Explicit representation and computation & Properties

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Overview

Definition

Floquet theory

Other types of Mathieu functions

Second kind

Explicit representation and computation

Properties

Applications

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Mathieu function

Nodes84
Edges83
Triples93
Avg. degree1.98
Density0.02381
Components1

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Mathieu function

Top relations

related to External links · 16
Mathieu function → EMS Press, Encyclopedia, EqWorldNIST Digital Library, Eric, Hill's Equation, Ideal, List, Mathematical Functions, Mathematics, Mathieu, Mathieu Functions, Mathieu's Equations, MathWorld, Paul Trap, Timothy Jones, Weisstein
related to Second kind · 11
Mathieu function → Bessel, Ce, Fe, Floquet's, Ge, Mathieu, One, Se, Since Mathieu's, The, There
related to Partial differential equations · 9
Mathieu function → Einstein, For, Helmholtz, In, Laplace, Mathieu, More, Since, Smoluchowski
related to Asymptotic expansions · 8
Mathieu function → Fe, Ge, Im, Mathieu, Re, Similar, The, Thus
related to Mathieu functions · 7
Mathieu function → As, In, Mathieu, More, The, They, When
related to Modified Mathieu functions · 6
Mathieu function → Accordingly, Ce, Closely, Mathieu, Mathieu's, Se
related to Orthogonality and completeness · 6
Mathieu function → Like, Liouville, Mathieu, Moreover, Sturm, This
related to Properties · 6
Mathieu function → Mathieu, Mathieu's, Moreover, Since, There, This
related to First kind · 5
Mathieu function → By, For, Fourier, Mathieu, The
related to Fractional order · 5
Mathieu function → An, If, In, Mathieu, See Ince's Theorem

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Important terminology

displaystyle mathieu equation functions solutions text ce se periodic one mathieu's characteristic order differential function solution modified kind pi numbers

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the quantum penduluminstance ofparticularly those with spatially periodic potentials0.80text
crystalline lattices.The modified Mathieu equation also arises when describing the quantum mechanics of singular potentialsinstance ofparticularly those with spatially periodic potentials0.80text
the S-matrixinstance ofscattering properties0.80text
the absorptivity can be obtained.Originally the Schrödinger equation with cosine function was solved in 1928 by Struttinstance ofscattering properties0.80text
Mathieu functionrelated to Asymptotic expansionsThe0.60section
Mathieu functionrelated to Asymptotic expansionsIm0.60section
Mathieu functionrelated to Asymptotic expansionsRe0.60section
Mathieu functionrelated to Asymptotic expansionsThus0.60section
Mathieu functionrelated to Asymptotic expansionsMathieu0.60section
Mathieu functionrelated to Asymptotic expansionsSimilar0.60section
Mathieu functionrelated to Asymptotic expansionsFe0.60section
Mathieu functionrelated to Asymptotic expansionsGe0.60section

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