Series expansions

Kapteyn series

Kapteyn series is a series expansion of analytic functions on a domain in terms of the Bessel function of the first kind. Kapteyn series are named after , who first studied such series in 1893. Let be a function analytic on the domain with . Then can be expanded in the form where The path of the integration is the boundary of . Here , and for , is defined by Kapteyn's series are important in physical problems. Among other applications, the solution of Kepler's equation can be expressed via a Kapteyn series: (Wikipedia).

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Related pages

Schlömilch's series