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arXiv · 1203.5550

The perturbed Bessel equation, I. A Duality Theorem

V. P. Gurarii·D. W. H. Gillam
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Abstract

The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation, and studying this equation separately from the differential equation by an appropriate Laplace-Borel technique, we associate with the latter equation another monodromic relation in the dual complex plane. This enables us to prove a duality theorem and to extend Goursat's formula to much larger classes of functions.

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V. P. Gurarii, D. W. H. Gillam. 2012-03-25. The perturbed Bessel equation, I. A Duality Theorem. https://doi.org/10.1016/j.jmaa.2013.06.033

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