Fourier series representation of Ferrers function P
Hans Volkmer
TL;DR
This paper analyzes the Fourier series expansion of the Ferrers function P of the first kind, focusing on its convergence properties and providing insights into its mathematical behavior.
Contribution
It presents a detailed analysis of the Fourier expansion of Ferrers function P, including the mode of convergence, which was not previously characterized.
Findings
Determined the mode of convergence of the Fourier series.
Provided explicit conditions for convergence.
Enhanced understanding of Ferrers function P's Fourier representation.
Abstract
In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.
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Taxonomy
TopicsMathematical functions and polynomials · Differential Equations and Boundary Problems · Analytic and geometric function theory