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 e~x 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 Power Series to prove e~(1/(m~(1/2)))、sin(1/(m~(1/2)))、cos(1/(m~(1/2))) are all Irrational number
引文
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