Abstract
The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities.We study the monodromic functional equation associated with a perturbation of the Bessel differential equation by means of a variant of the Laplace–Borel technique: we introduce and study a related monodromic equation in the dual complex plane. This construction is a crucial element in our proof of a duality theorem that leads to an extension of the Euler–Gauss–Goursat formula for hypergeometric functions to a substantially larger class of functions.
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