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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.
Whittaker–Hill equation. Add languages. Add links. ... Upload file; Special pages ... Get shortened URL; Download QR code; Print/export Download as PDF; Printable ...
Title page for the third edition of the book. A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions (colloquially known as Whittaker and Watson) is a landmark textbook on mathematical analysis written by Edmund T. Whittaker and George N. Watson, first published by Cambridge ...
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.
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 ...
The book's structure remained constant throughout its development, with fifteen total chapters, though the second and third editions added new sections throughout. [9] Among other changes to the book, Whittaker expanded chapters fifteen and sixteen considerably and renamed chapters nine and sixteen. [9]
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 ...