德拜函数

德拜函数(Debye function)是彼得·德拜于1912年估算声子对固体的比热德拜模型时创立的函数,定义如下

德拜函数
展开式

其中伯努利数

[1]

其中是m阶多重对数

渐近式

For :

For : : [2]

相关函数

Debye function Maple complex3D animation

也有将德拜函数定义为[3]

参考文献

  1. A. E. Dubinov, A. A. Dubinova ,Exact integral-free expressions for the integral Debye functions,Technical Physics Letters,December 2008, Volume 34, Issue 12, pp 999-1001
  2. Gradshteyn, I. S., & Ryzhik, I. M. (1980). Table of integrals. Series, and Products (Academic, New York, 1980), (3.411).
  3. Milton abramowitz Irene Stegun, Handbook of Mathematical Functions,National Bureau of Standards, p998 1972
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