关于函数Li(x)=dt/lnt,x∈[1,990000] integral from n=0 to x的数值表

Numerical value table of the function Li(x)=dt/lnt,x∈[1,990000] integral from n=0 to x

目的在数理科学的一些领域,常用到函数Li(x)的数值,如在数论中,素数在实数中的分布就与此函数值有关,但此函数的计算性质非常复杂,很难进行实际运算,而且在文献中尚未给出此函数的数值表。为了使用方便,计算此函数对x∈[1,990 000]的数值,给出其对数积分函数的数值表便是本文的目的所在。方法按照Gregory数值积分公式,在梯形规则近似下的累加方法进行研究。结果由于x在[1,990 000]区间取值所得Li(x)的函数值非常庞大,不可能全部列出,仅给出Li(x)函数值的5个简表(x=j.10k×i.10k-1,k=1,2,3,4,5)。结论计算误差约小于0.01,表1中x∈[1,99],表2中x∈[100,990],表3中x∈[1 000,9 900],表4中x∈[10 000,99 000]以及表5中x∈[100 000,990 000]。

Aim In some fields of the mathematical and physical science, it is usual to us the numerical values of the function Li （x）. For example, in the number theory, the distribution of the prime number in the real number is connected with the numerical values of the function Li（x）. The property of the function Li（x）＇s computability is very complicated. It is very difficult to compute really. And the numerical value table of the function Li （x） in the documents published is unobserved. For ease of use, the numerical values of the function Li（x） （x ∈ [1, 990 0007） were computed. Methods According to Gregory numerical integration formula, in the trapezoidal rule approximation of the cumulative method is used. Results Because the numerical values of Li（x） （x∈ [1, 990 000]） are monumental, here, five abridged tables in total were only given, x =j · 10^k ×i· 10^k-1 , k = 1, 2, 3, 4, 5. Conclusion The errors are less than 0.01. Table i （ x ∈ [1,99] ）, Table 2 （ x ∈ [100,990] ）, Table 3 （ x ∈[1 000,9 900] ）, Table 4（ x ∈ [10 000,99 000] ） and Table 5 （ x ∈ [100 000,990 000] ） were given.