{"data":{"id":"10.4231/r7b8562s","type":"dois","attributes":{"doi":"10.4231/r7b8562s","prefix":"10.4231","suffix":"r7b8562s","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Gautschi, Walter","givenName":"Walter","familyName":"Gautschi","affiliation":["Purdue University"],"nameIdentifiers":[{"schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0000-0001-9184-8899","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"MCD: Matlab programs for computing the Macdonald function for complex orders"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"Computer Science"},{"subject":"Macdonald function"},{"subject":"modified Bessel function"},{"subject":"complex order"},{"subject":"Gauss quadrature approximation"},{"subject":"Matlab software"},{"subject":"FORTRAN"},{"subject":"Quadrature and cubature formulas"},{"subject":"Software source code"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Walter Gautschi Archives"}],"contributors":[],"dates":[{"date":"2014-04-22","dateType":"Available"},{"date":"2014-04-22","dateType":"Submitted"},{"date":"2014-04-23","dateType":"Accepted"},{"date":"2014","dateType":"Issued"}],"language":"en","types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Datasets","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"10.1007/s10543-005-0020-5","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["9 files","13 KB"],"formats":["text/plain","text/x-fortran"],"version":"1.0","rightsList":[{"rights":"Creative Commons Zero v1.0 Universal","rightsUri":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc0-1.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"\u0026lt;p\u0026gt;The use of Gaussian quadrature formulae is explored for the computation of the Macdonald function (modified Bessel function) of complex orders and positive arguments. It is shown that for arguments larger than one, Gaussian quadrature applied to the integral representation of this function is a viable approach, provided the (nonclassical) weight function is suitably chosen. In combination with Gauss\u0026amp;ndash;Legendre quadrature the approach works also for arguments smaller than one. For very small arguments, power series can be used. A Matlab routine is provided that implements this approach.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"A collection of FORTRAN and Matlab codes and their outputs to compute the Macdonald function for complex orders by numerical quadrature.","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://purr.purdue.edu/publications/1561/1","contentUrl":null,"metadataVersion":8,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-04-22T15:44:16.000Z","registered":"2014-04-22T15:44:17.000Z","published":"2014","updated":"2025-12-18T19:40:57.000Z"},"relationships":{"client":{"data":{"id":"purdue.purduelib","type":"clients"}},"provider":{"data":{"id":"purdue","type":"providers"}},"media":{"data":{"id":"10.4231/r7b8562s","type":"media"}},"references":{"data":[{"id":"10.1007/s10543-005-0020-5","type":"dois"}]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}