On Ruby's solid angle formula and some of its generalizations
Samuel Friot
TL;DR
This paper presents a new representation of Ruby's solid angle formula and its generalizations using Mellin-Barnes integrals, expressing them with Appell F4 and Lauricella Fc functions.
Contribution
It introduces a compact formulation of Ruby's solid angle formula and its generalizations via special functions using Mellin-Barnes representation.
Findings
Expressed Ruby's solid angle formula with Appell F4 functions
Generalized the formula using Lauricella Fc functions
Provided a unified Mellin-Barnes integral representation
Abstract
Using the Mellin-Barnes representation, we show that Ruby's solid angle formula and some of its generalizations may be expressed in a compact way in terms of the Appell F4 and Lauricella Fc functions.
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