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Revisiting Ramanujan’s Master Theorem

2026-07Artigo científico Acesso aberto
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dc.contributor.authorOrtigueira, Manuel Duarte
dc.contributor.authorBengochea, Gabriel
dc.contributor.institutionCTS - Centro de Tecnologia e Sistemas
dc.contributor.institutionUNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
dc.contributor.pblMDPI - Multidisciplinary Digital Publishing Institute
dc.date.accessioned2026-09-04T13:39:01Z
dc.date.available2026-09-04T13:39:01Z
dc.date.issued2026-07
dc.descriptionThe first author was funded by Portuguese National Funds through the FCT—Foundation for Science and Technology—within the scope of the CTS Research Unit—Center of Technology and Systems/UNINOVA/FCT/NOVA—under reference UIDB/00066/2025. The second author was supported by the Autonomous University of Mexico City (UACM) under reference UACM CCYT2026-CON-01. Publisher Copyright: © 2026 by the authors.
dc.description.abstractRamanujan’s master theorem is considered to express particular values of the Liouville fractional derivatives. This fact is used to immediately obtain generalizations. Firstly, it is shown that the original formulation is suitable only for anti-causal functions. Consequently, an expression for causal functions is introduced. Secondly, the two formulations are extended to be valid for any real order and related to the Laplace transform, corresponding to transforms with left- or right-sided regions of convergence. This leads to introducing the concept of the unilateral MacLaurin series and the substitution of the Liouville derivative by the (Liouville–)Grünwald–Letnikov derivative, which essentially expresses a discrete formulation that is suitable for numerical implementations. The way in which this procedure arose and its relationship with the Liouville derivatives suggested other approaches, which are briefly discussed, such as replacing the MacLaurin series with the Mittag–Leffler series or the Liouville derivative with the Riesz, Feller, or Hadamard derivatives.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent18
dc.format.extent318581
dc.identifier.doi10.3390/sym18071208
dc.identifier.issn2073-8994
dc.identifier.otherPURE: 172516712
dc.identifier.otherPURE UUID: 97bd0640-b401-4512-ba00-2919b09be800
dc.identifier.otherScopus: 105045905432
dc.identifier.otherORCID: /0000-0003-4270-3284/work/225839387
dc.identifier.urihttp://hdl.handle.net/10362/206104
dc.identifier.urlhttps://www.scopus.com/pages/publications/105045905432
dc.language.isoeng
dc.peerreviewedyes
dc.subjectGrünwald–Letnikov derivative
dc.subjectLiouville derivative
dc.subjectRamanujan’s master theorem
dc.subjectComputer Science (miscellaneous)
dc.subjectChemistry (miscellaneous)
dc.subjectGeneral Mathematics
dc.subjectPhysics and Astronomy (miscellaneous)
dc.titleRevisiting Ramanujan’s Master Theoremen
dc.typejournal article
degois.publication.issue7
degois.publication.titleSymmetry
degois.publication.volume18
dspace.entity.typePublication
rcaap.rightsopenAccess

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