拉马努金积分及其导数:计算与分析

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2023-08-15 DOI:10.1090/mcom/3892
Walter Gautschi, Gradimir Milovanovic
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引用次数: 0

摘要

本文使用的主要计算工具是区间[0,1]上的经典高斯正交,它在这里特别有效。得到了所讨论的Ramanujan积分的导数的显式表达式,并证明了Ramanujan积分在(0,∞)(0,\infty)上是完全单调的。作为一个副产品,已知的不完全函数的级数展开式是关于其收敛性的。本文还关注了另一个著名的积分,欧拉积分-更广为人知的是伽马函数-重新激活了函数中很大程度上被忽视的部分,即对应于参数负值的部分,这部分在我们的工作中起着突出的作用。
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A Ramanujan integral and its derivatives: computation and analysis
The principal tool of computation used in this paper is classical Gaussian quadrature on the interval [0,1], which happens to be particularly effective here. Explicit expressions are found for the derivatives of the Ramanujan integral in question, and it is proved that the latter is completely monotone on ( 0 , ) (0,\infty ) . As a byproduct, known series expansions for incomplete gamma functions are examined with regard to their convergence properties. The paper also pays attention to another famous integral, the Euler integral — better known as the gamma function — revitalizing a largely neglected part of the function, the part corresponding to negative values of the argument, which plays a prominent role in our work.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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