Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Functions for Statistics

统计学中的函数

A form of integral which shows up regularly in quantum statistics is

在量子统计中经常出现的一种积分形式是

The evaluation of this class of integrals is in terms of two special functions, the gamma function and the Riemann zeta function.

这类积分的求解涉及两个特殊函数,即伽马函数和黎曼齐次函数。
Index

Statistics concepts

Reference
Schroeder
App. B
索引 统计概念 参考 Schröder 附录 B
 
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The Gamma Function

Gamma 函数

A function which shows up often in statistical calculations is the gamma function:

在统计计算中经常出现的一个函数是伽马函数:

This can be related to another integral

这可以与另一个积分相关联

leading to the relationships

导致关系式

Some other common relationships with gamma functions:

一些与伽马函数相关的其他常见关系:

One of the applications of the gamma function is in the evaluation of statistical integrals.

伽马函数的一个应用是在统计积分的计算中。
Index

Statistics concepts

Reference
Schroeder
App. B
索引 统计概念 参考 Schröder 附录 B
 
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The Riemann Zeta Function

黎曼ζ函数

A function which shows up often in statistical calculations is the Riemann zeta function:

在统计计算中经常出现的一个函数是黎曼ζ函数:

One of the applications of the zeta function is in the evaluation of statistical integrals.

ζ函数的一个应用是在统计积分的计算中。
Index

Statistics concepts

Reference
Schroeder
App. B
索引 统计概念 参考 Schröder 附录 B
 
HyperPhysics*****HyperMathR Nave
Go Back
返回