Euler–Goursat-like formula via Laplace–Borel duality

The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities. dy 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.