广义反应速率积分作为一般微分方程的解
Extended Reaction Rate Integral as Solutions of Some General Differential Equations
摘要：
本文考虑了在非共振热核反应中，当核尾贫化和右尾截断时，反应速率概率积分的一种推广形式。反应速率积分可以看作是非广延统计力学的Tsallis型统计量和拉伸指数的Mellin变换的卷积的逆，以及超统计量和拉伸指数的Mellin变换的卷积的逆。导出了广义概率积分所满足的微分方程。该方法采用了一种新颖的思想，即先用一些特殊函数来计算延拓积分，然后再调用这些特殊函数所满足的微分方程。还讨论了极限情况的一些特殊情况。
英文摘要：
Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the inverse of the convolution of the Mellin transforms of Tsallis type statistics of nonextensive statistical mechanics and stretched exponential as well as that of superstatistics and stretched exponentials. The differential equations satisfied by the extended probability integrals are derived. The idea used is a novel one of evaluating the extended integrals in terms of some special functions and then by invoking the differential equations satisfied by these special functions. Some special cases of limiting situations are also discussed.
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