doi:10.1002/mma.9939engDurán, Antonio J.Pérez, MarioVarona, Juan LuisSumming Sneddon–Bessel series explicitlyART-2024-137579We sum in a closed form the Sneddon–Bessel series [fórmula] where 0 < X, 0 < y, x + y < 2, n is an integer, [fórmula] with [fórmula] and [fórmula] are the zeros of the Bessel function [fórmula] of order [fórmula]. In most cases, the explicit expressions for these sums involve hypergeometric functions [fórmula]. As an application, we prove some extensions of the Kneser–Sommerfeld expansion. For instance, we show that [fórmula] if Re v < Re B + 1 and [fórmula](here, Yv denotes the Bessel function of the second kind), which becomes the Kneser–Sommerfeld expansion when B = v.2024http://zaguan.unizar.es/record/13244010.1002/mma.9939http://zaguan.unizar.es/record/132440oai:zaguan.unizar.es:132440info:eu-repo/grantAgreement/ES/AEI/PID2021-124332NB-C21info:eu-repo/grantAgreement/ES/AEI/PID2021-124332NB-C22info:eu-repo/grantAgreement/ES/DGA/E48-23RMathematical Methods in the Applied Sciences 47, 7 (2024), 6590-6606byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess