{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:06:22Z","timestamp":1773230782621,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:p>Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators, and present a generalized Hermite\u2013Genocchi formula. This formula then allows the definition of a larger class of fractional B-splines.<\/jats:p>","DOI":"10.1142\/s0219691308002343","type":"journal-article","created":{"date-parts":[[2008,3,25]],"date-time":"2008-03-25T12:05:59Z","timestamp":1206446759000},"page":"279-290","source":"Crossref","is-referenced-by-count":4,"title":["SOME REMARKS ABOUT THE CONNECTION BETWEEN FRACTIONAL DIVIDED DIFFERENCES, FRACTIONAL B-SPLINES, AND THE HERMITE\u2013GENOCCHI FORMULA"],"prefix":"10.1142","volume":"06","author":[{"given":"PETER","family":"MASSOPUST","sequence":"first","affiliation":[{"name":"Institute for Biomathematics and Biometry, Helmholtz Zentrum M\u00fcnchen \u2013 German Research Center for Environment and Health, Ingolst\u00e4dter Landstra\u00dfe 1, DE\u201385764 Neuherberg, Germany"}]},{"given":"BRIGITTE","family":"FORSTER","sequence":"additional","affiliation":[{"name":"Center for Mathematical Sciences, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstr. 3, DE\u201385747 Garching, Germany"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325937"},{"key":"rf2","volume-title":"Wahrscheinlichkeitstheorie","author":"Bauer H.","year":"2002"},{"key":"rf3","volume-title":"Special Functions of Applied Mathematics","author":"Carlson B. C.","year":"1977"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/059\/870446"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/2005825"},{"key":"rf6","first-page":"281","volume":"20","author":"Forster B.","journal-title":"Appl. Comp. Harmon. Anal."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1988-0929549-2"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/68.1.165"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1980-0572866-1"},{"key":"rf10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1975.tb01024.x","volume":"37","author":"Kingman J. F. C.","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"key":"rf11","volume-title":"Poisson Processes","author":"Kingman J. F. C.","year":"1993"},{"key":"rf12","volume-title":"Wahrscheinlichkeitstheorie","author":"Klenke A.","year":"2006"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1137\/1018042"},{"key":"rf14","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller K. S.","year":"1993"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1979-0516462-4"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0018-0"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598349435"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1137\/1122006"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691308002343","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T06:38:18Z","timestamp":1738132698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691308002343"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":18,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2008,3]]}},"alternative-id":["10.1142\/S0219691308002343"],"URL":"https:\/\/doi.org\/10.1142\/s0219691308002343","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}