查看“︁希沃特积分”︁的源代码

{{noteTA
|1=zh-tw:西弗;zh-hk:希沃特;zh-cn:希沃特;
|2=zh-tw:羅爾夫·馬克西米連·西弗;zh-hk:羅爾夫·馬克西米利安·希沃特;
}}
[[File:Sievert Integral.gif|thumb|300px|Sievert Integral]]
'''希沃特积分'''(Sievert Integral)是用于模拟[[放射性]]剂量的一种[[特殊函数]]，为[[瑞典]]醫學物理師[[羅爾夫·馬克西米利安·希沃特]]（{{lang-sv|Rolf Maximilian Sievert}}）所推得，[[輻射轉移]]定义如下：<ref> R. M. Sievert Die Intensitätsverteilung der primären γ-Strahlung in der Nähe medizinischer Radiumpräparate (нем.) // Acta Radiologica. — 1921. — Т. 1. — № 1. — С. 89-128.</ref><ref>Abramowitz, Milton; Stegun, Irene A., eds. (1965), "Chapter 27", Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, p. 1001, ISBN 978-0486612720</ref>

<math>S(x,\theta)=\int_{0}^{\theta}e^{-xsec(\phi)}d\phi</math>

==关系式==
<math>S(x,\theta)\approx  \sqrt{\frac{\pi}{2x}}e^{-x}erf(\sqrt{\frac{x}{2}}\theta)</math>

<math>S(x,\pi/2)=BesselK(1,x)</math>
==级数展开==
*<math>S(x,\frac{\pi}{5}  ) \approx {.628-.674*x+.364*x^2-.131*x^3+0.357e-1*x^4-0.780e-2*x^5+0.143e-2*x^6-0.225e-3*x^7+0.310e-4*x^8-0.368e-5*x^9+O(x^10)}</math>

*<math>S( 3,  \theta) \approx {0.498e-1*\theta-0.249e-1*\theta^3+0.498e-2*\theta^5+0.862e-3*\theta^7-0.104e-3*\theta^9-0.857e-4*\theta^11-0.222e-4*\theta^13-0.155e-5*\theta^15+O(\theta^17)}</math>

==参考文献==
<references/>

[[Category:特殊函数]]