{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:25Z","timestamp":1777447945865,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T00:00:00Z","timestamp":1544400000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2019,1,1]]},"abstract":"<jats:p>We give an extended Pizzetti asymptotic formula, namely, we show that if \u03d5 is smooth in an open set that contains the origin in [Formula: see text] and if p is a harmonic homogeneous polynomial of degree k, then [Formula: see text] as [Formula: see text] for some constants C and [Formula: see text] that are given in the text. We also show that the formula never holds, for all \u03d5, if p is not harmonic.<\/jats:p>\n                  <jats:p>We consider two procedures, one algebraic and the other analytic, to find the part of an object \u2013 a formal power series or a smooth function \u2013 that is a radial multiple of a given polynomial and show that the two constructions yield the same results for harmonic polynomials but not otherwise.<\/jats:p>\n                  <jats:p>We also consider mean value type results for solutions of partial differential equations, including a version of Morera\u2019s theorem that applies to locally integrable functions.<\/jats:p>","DOI":"10.3233\/asy-181483","type":"journal-article","created":{"date-parts":[[2018,12,11]],"date-time":"2018-12-11T11:50:53Z","timestamp":1544529053000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On Pizzetti\u2019s formula"],"prefix":"10.1177","volume":"111","author":[{"given":"Ricardo","family":"Estrada","sequence":"first","affiliation":[{"name":"Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2018,12,10]]},"reference":[{"key":"ref001","first-page":"41","volume":"17","author":"Aguirre M.A.","year":"1997","journal-title":"Bol. Soc. Parana. Mat."},{"key":"ref002","first-page":"120","volume":"187","author":"Aguirre M.A.","year":"2007","journal-title":"Appl. Math. 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