{"title":"A Note on Gamma Functions","authors":"G. N. Watson","doi":"10.1017/S0950184300003207","DOIUrl":"https://doi.org/10.1017/S0950184300003207","url":null,"abstract":"Various improvements in the formula which was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122178263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Electrostatic Energy of a Two-Dimensional System","authors":"L. Chambers","doi":"10.1017/S0950184300003189","DOIUrl":"https://doi.org/10.1017/S0950184300003189","url":null,"abstract":"The use of the complex variable z ( = x + iy ) and the complex potential W (= U + iV ) for two-dimensional electrostatic systems is well known and the actual system in the ( x , y ) plane has an image system in the ( U , V ) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the ( U , V ) plane.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127448856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Number Problem","authors":"N. Y. Wilson","doi":"10.1017/S0950184300003219","DOIUrl":"https://doi.org/10.1017/S0950184300003219","url":null,"abstract":"A THEOREM ON POWER SUMS 161 We summarize these results in the following. Theorem. The solutions of (2) are as follows. If p = q, f(x) is a r b i-trary and g(x) = f(x). If p ^ q, the only monic solutions occur when p = 2 and q = 1, in which case f(x) and g(x) are defined by (12), where a is an arbitrary real constant Non-monic solutions for that case can be found using (13). As an example of these results suppose that p = 3 and q = 4. By (14) and (17) we have 13 (n , 4 (3x 2-3x + 1) J , (n = 1, 2, 3, • • •) x=l 1 x=l ' (4X 3-6x 2 + 4x-1) There are infinite many numbers with the property: if units digit of a positive integer, M, is 6 and this is taken from its place and put on the left of the remaining digits of M, then a new integer, N, will be formed, such that N = 6M. The smallest M for which this is possible is a number with 58 digits (1016949 • • • 677966). 1-4x-x 2 n=o with x = 0,1 we have 1,01016949 * • • 677966, where the period number (behind the first zero) is M.*","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117230114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Rule for Resolving Integral Algebraic Expressions into Factors","authors":"R. Muirhead","doi":"10.1017/S1757748900000591","DOIUrl":"https://doi.org/10.1017/S1757748900000591","url":null,"abstract":"Professor Chrystal remarks (Algebra, Chap. VII. §4) that “for tntative processes no general rule can be given.” The tentative processes consist in arranging the terms in groups in such a way as either to manifest a factor common to these groups or aggregates of terms, or to bring the expression under one of the Standard Forms of which the factors are already known, such as a 2 - b 2 , a 3 - b 3 , a 3 + b 3 .","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1910-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121034432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Wallis' formula","authors":"D. K. Kazarinoff","doi":"10.1017/S095018430000029X","DOIUrl":"https://doi.org/10.1017/S095018430000029X","url":null,"abstract":"In the course of mathematical progress new truths are discovered while older ones are sometimes more precisely articulated and often generalised. Because of their elegance and simplicity, however, some classical statements have been left unchanged. As an example, I have in mind the celebrated formula of John Wallis, which for more than a century has been quoted by writers of textbooks. Usually this formula is written as In this note it is shown that ¼","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122773895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A property of quartic curves with two cusps and one node","authors":"E. Primrose","doi":"10.1017/S0950184300003062","DOIUrl":"https://doi.org/10.1017/S0950184300003062","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114853138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On certain modular determinants","authors":"H. W. Turnbull","doi":"10.1017/S095018430000269X","DOIUrl":"https://doi.org/10.1017/S095018430000269X","url":null,"abstract":"y1 = 0, y2 is negative o r 2/i = 2/2 = 2/3 = 0, 2/4 is negative o r 2/1=2/2 = 2/3 = 2/4 = 2/5 = °. Vo is negative, etc. Further the relation between the sign of dy/dx and the concavity of an arc is often obscurely presented. Take an x or time axis horizontally and a y axis vertically and consider an arc AB everywhere concave down. Let C be a point on the arc such that AC and CB have equal horizontal projections, and let their vertical projections be ac and cb. Then algebraically we have from a figure ac > cb, that is, heights gained in equal successive times are diminishing and therefore there is a retardation and d'-y/dx is negative. And we similarly associate concavity upwards with positive values of* d-y/dx.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132243525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
求助内容：
应助结果提醒方式：