{"title":"Wallis比率幂的基本渐近估计","authors":"V. Lampret","doi":"10.4067/s0719-06462021000300357","DOIUrl":null,"url":null,"abstract":"For any a ∈ R , for every n ∈ N , and for n -th Wallis’ ratio w n := (cid:81) nk =1 2 k − 1 2 k , the relative error r 0 ( a, n ) := (cid:0) v 0 ( a, n ) − w an (cid:1) /w an of the approximation w an ≈ v 0 ( a, n ) := ( πn ) − a/ 2 is estimated as (cid:12)(cid:12) r 0 ( a, n ) (cid:12)(cid:12) < 14 n . The improvement w an ≈ v ( a, n ) := ( πn ) − a/ 2 (cid:16) 1 − a 8 n + a 2 128 n 2 (cid:17) is also studied.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Basic asymptotic estimates for powers of Wallis’ ratios\",\"authors\":\"V. Lampret\",\"doi\":\"10.4067/s0719-06462021000300357\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any a ∈ R , for every n ∈ N , and for n -th Wallis’ ratio w n := (cid:81) nk =1 2 k − 1 2 k , the relative error r 0 ( a, n ) := (cid:0) v 0 ( a, n ) − w an (cid:1) /w an of the approximation w an ≈ v 0 ( a, n ) := ( πn ) − a/ 2 is estimated as (cid:12)(cid:12) r 0 ( a, n ) (cid:12)(cid:12) < 14 n . The improvement w an ≈ v ( a, n ) := ( πn ) − a/ 2 (cid:16) 1 − a 8 n + a 2 128 n 2 (cid:17) is also studied.\",\"PeriodicalId\":36416,\"journal\":{\"name\":\"Cubo\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cubo\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4067/s0719-06462021000300357\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cubo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4067/s0719-06462021000300357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
为任何a∈R,因为每n∈n, and For -th沃利斯“ratio w n = (cid): 81) nk k = 1 2 k−1,亲戚错误R 0杂志》(a, n): = (cid) v 0 (a, n) w−an (cid》:1)/ w的类似w v≈0的(a, n): =(π)−a / 2是美国estimated (cid 12: 12) (cid) R 0 (a, n) (cid: 12 (cid): 12) < 14 n。安improvement w v≈杂志》(a, n): =(πa / 2 (n)−cid: 16) 1−a 8 n + 2 128 n (cid: 17)是也studied。
Basic asymptotic estimates for powers of Wallis’ ratios
For any a ∈ R , for every n ∈ N , and for n -th Wallis’ ratio w n := (cid:81) nk =1 2 k − 1 2 k , the relative error r 0 ( a, n ) := (cid:0) v 0 ( a, n ) − w an (cid:1) /w an of the approximation w an ≈ v 0 ( a, n ) := ( πn ) − a/ 2 is estimated as (cid:12)(cid:12) r 0 ( a, n ) (cid:12)(cid:12) < 14 n . The improvement w an ≈ v ( a, n ) := ( πn ) − a/ 2 (cid:16) 1 − a 8 n + a 2 128 n 2 (cid:17) is also studied.
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