e^(1/(m^(1/2)))、sin(1/(m^(1/2)))、cos(1/(m^(1/2)))都是无理数  

e^(1/(m^(1/2)))、sin(1/(m^(1/2)))、cos(1/(m^(1/2))) are All Irrational Number

作　　者：东洪平[1] 邱晓鹏[1] 

机构地区：[1]陇南师范高等专科学校数信学院,甘肃成县742500

出　　处：《甘肃高师学报》2017年第3期12-15,共4页Journal of Gansu Normal Colleges

基　　金：陇南市科技计划项目"对一个古典数学问题的推进"(2016-27)

摘　　要：当x是非零有理数时,e^x是无理数,已被数学家兰伯特(J.Lambert)于1771年证明.当x是无理数时,e^x是有理数还是无理数,至今无人解决.利用幂级数证明了e^(1/(m^(1/2)))、sin(1/(m^(1/2)))、cos(1/(m^(1/2)))(m=1,2,3,…)都是无理数.Mathematician J . Lambert had proved ex is a Irrational number When x is a non-zero rational number in 1771.But When is a Irrational number, is a rational number or Irrational number,e^x nobody had proved this question till now. This article will use e^（1/（m^（1/2）））、sin（1/（m^（1/2）））、cos（1/（m^（1/2）））are all Irrational number

关 键 词：幂级数 e^(1/(m^(1/2)))、sin(1/(m^(1/2)))、cos(1/(m^(1/2))) 无理数 

分 类 号：O156.1[理学—数学]