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In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation ′ ′ + ′ + ( ()) = When p is a non-negative integer, it has polynomial solutions called Ince polynomials.
Prof Edward Lindsay Ince FRSE (30 November 1891 – 16 March 1941) was a British mathematician who worked on differential equations, especially those with periodic coefficients such as the Mathieu equation and the Lamé equation. He introduced the Ince equation, a generalization of the Mathieu equation.
Plot of the Whittaker function M k,m(z) with k=2 and m= 1 / 2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker () to make the formulas involving the solutions more ...
The math template formats mathematical formulas generated using HTML or wiki markup. (It does not accept the AMS-LaTeX markup that <math> does.) The template uses the texhtml class by default for inline text style formulas, which aims to match the size of the serif font with the surrounding sans-serif font (see below).
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Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of (), solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. [3] The precise form of the solutions to Hill's equation is described by Floquet theory. Solutions ...
Tricomi's (confluent hypergeometric) function U(a, b, z) introduced by Francesco Tricomi , sometimes denoted by Ψ(a; b; z), is another solution to Kummer's equation. This is also known as the confluent hypergeometric function of the second kind. Whittaker functions (for Edmund Taylor Whittaker) are solutions to Whittaker's equation.
A rank abundance curve or Whittaker plot is a chart used by ecologists to display relative species abundance, a component of biodiversity. It can also be used to visualize species richness and species evenness. It overcomes the shortcomings of biodiversity indices that cannot display the relative role different variables played in their ...