| 李世才,吴戈堂,林莺.Γ分布函数算法新解及其应用[J].水利学报,1999,30(12):0070-0078 |
| Γ分布函数算法新解及其应用 |
| New Interpretation of the Algorithm and Its Application for Γ-Distribution Function |
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| DOI： |
| 中文关键词: Γ函数 Γ分布函数 算法新解 精确解析式 数学模型 数值计算 |
| 英文关键词: Γ function Γ distribution function new interpretation of the algorithm the exact analytic expression mathematical model numerical evaluation |
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| 摘要点击次数: 2378 |
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| 中文摘要: |
| 从Γ函数与不完全Γ函数的恒等关系出发，导出了Γ(α)与lnΓ(α)的精确解析式，并在文[1]的基础上导出Γ分布函数新算法的精确解析式。把迄今Γ(α)、lnΓ(α)和Γ分布函数的计算只能应用各种逼近的近似公式现状，提高到精确解析式的计算水平，并归纳为收敛的级数展式和连分式展式的数值计算，使其算法统一成为现实。用新算法的通用数学模型设计的电算程序，对实际工程的计算和文[2～4]中的全部算例及文[5，6]中的有关数表进行了验证比较，结果表明新算法更为优越。 |
| 英文摘要: |
| Proceeding from the identically equal of Γ-function and incomplete Γ-function, this paper calculate the exact analytic expression of Γ(α) and ln Γ(α), and calculate the exact analytic expression of new algorithm for Γ-distribution function based on the reference[1]。Promoting the existing calculation for Γ(α),ln Γ(α) and Γ distribution function by varied approximate formula so far to the level of calculation by exact analytic expression, and sum up to the numerical evaluation of convergent series and continued fraction expansion, make the unity of their algorithm into reality. The programme designed by the general mathematical model of new algorithm has check some actual project, all example in reference[2～4] and some numeration table in reference[5,6], and the new algorithm has verified be more superior. |
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