{"title":"关于函数G0(x)、G1(x)、Jn(x√¯i)的数值计算","authors":"W. S. Aldis","doi":"10.1098/rspl.1899.0069","DOIUrl":null,"url":null,"abstract":"1. The complete solution of the equation d2y/dx2 + 1/x · dy/dx ‒ (1+n2/x2)y = 0 May be written y = AIn(x)+BKn(x), where In(x) = ∑r=∞ r=0 (1/2x)n+2r/ II (r). II (n+r) ........ (1) ;","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1899.0069","citationCount":"0","resultStr":"{\"title\":\"On the numerical computation of the functions G0(x), G1(x), and Jn(x√¯i)\",\"authors\":\"W. S. Aldis\",\"doi\":\"10.1098/rspl.1899.0069\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1. The complete solution of the equation d2y/dx2 + 1/x · dy/dx ‒ (1+n2/x2)y = 0 May be written y = AIn(x)+BKn(x), where In(x) = ∑r=∞ r=0 (1/2x)n+2r/ II (r). II (n+r) ........ (1) ;\",\"PeriodicalId\":20661,\"journal\":{\"name\":\"Proceedings of the Royal Society of London\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1098/rspl.1899.0069\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspl.1899.0069\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspl.1899.0069","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
1. 方程d2y/dx2 + 1/x·dy/dx - (1+n2/x2)y =0的完全解可以写成y = AIn(x)+BKn(x),其中In(x) =∑r=∞r=0 (1/2x)n+2r/ II (r). II (n+r) ........(1);
On the numerical computation of the functions G0(x), G1(x), and Jn(x√¯i)
1. The complete solution of the equation d2y/dx2 + 1/x · dy/dx ‒ (1+n2/x2)y = 0 May be written y = AIn(x)+BKn(x), where In(x) = ∑r=∞ r=0 (1/2x)n+2r/ II (r). II (n+r) ........ (1) ;