{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T20:51:15Z","timestamp":1754599875567,"version":"3.37.3"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,11,4]],"date-time":"2018-11-04T00:00:00Z","timestamp":1541289600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["OE\/EME\/LA0022"],"award-info":[{"award-number":["OE\/EME\/LA0022"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Mathematical Physics"],"published-print":{"date-parts":[[2018,11,4]]},"abstract":"<jats:p>The original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differential equation are obtained for all possible combinations of the two complex parameters, order and degree, and finite complex variable, as Frobenius-Fuchs series around the regular singularity at the origin; the series converge in the whole complex plane of the variable, except for the point-at-infinity, that is, the only other singularity of the differential equation. The regular integral solutions of the first and second kinds lead, respectively, to the generalized Bessel and Neumann functions; these reduce to the original Bessel and Neumann functions for zero degree and have alternative expressions for nonzero degree.<\/jats:p>","DOI":"10.1155\/2018\/8919516","type":"journal-article","created":{"date-parts":[[2018,11,4]],"date-time":"2018-11-04T18:31:45Z","timestamp":1541356305000},"page":"1-9","source":"Crossref","is-referenced-by-count":4,"title":["On the Regular Integral Solutions of a Generalized Bessel Differential Equation"],"prefix":"10.1155","volume":"2018","author":[{"given":"L. M. B. C.","family":"Campos","sequence":"first","affiliation":[{"name":"Center for Aeronautical and Space Science and Technology (CCTAE), IDMEC, LAETA, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. 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