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1 Euler常数问题的提出关于调和级数1+1/2+1/3+…+1/n+…的发散问题,雅谷-伯努利早在1689～1704年曾有多篇文章论述,其学生Euler以其数学的敏锐和犀利的目光发现了1+1/2+1/3+…+1/n+…与lnn之间竟有那么密切的联系,他发现c=(?)[(1+1/2+1/3+…+1/n)-lnn]存在,并算到小数点后第5位(c=0.57721),这就是著名的欧拉-马歇罗尼常数c,该结论在数论中应用极广,常见的有极限、级数、积分三种表达式.到1974年止,人
1 The Euler’s constant problem has been raised. As far as the divergence problem of the harmonic series 1+1/2+1/3+...+1/n+..., Yagyu-Bernoulli had already discussed several articles from 1689 to 1704. Student Euler discovered with his mathematical keenness and sharp eyes that 1+1/2+1/3+...+1/n+... was so closely related to lnn that he found c=(?)[(1 +1/2+1/3+...+1/n)-lnn] exists and counts to the 5th decimal place (c=0.57721). This is the famous Euler-Mascheroni constant c. It is widely used in number theory. There are three expressions: limit, series, and integral. By 1974, people