查看“︁Chi函数”︁的源代码

'''Chi 函数'''定义如下<ref>Abramowitz, M. and Stegun, I. A. (Eds.). "Sine and Cosine Integrals." §5.2 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 231-233, 1972. </ref><ref>
Sloane, N. J. A. Sequence A061079 in "The On-Line Encyclopedia of Integer Sequences</ref>

[[File:Chi(x) 2D plot.png|thumb|300px|Chi(x) 2D plot]]
[[File:Chi(x) 3D plot.png|thumb|300px|Chi(x) 3D plot]]
<math>{\it Chi} \left( z \right) =\int _{0}^{z}\!{\frac {\cosh \left( t \right) }{t}}{dt}</math>

<math>Chi(z)</math> 是下列三阶非线性常微分方程的一个解:

<math>z{\frac {d}{dz}}w \left( z \right) -2\,{\frac {d^{2}}{d{z}^{2}}}w
 \left( z \right) -z{\frac {d^{3}}{d{z}^{3}}}w \left( z \right) =0</math>

即：

<math>w \left( z \right) ={\it \_C1}+{\it \_C2}\,{\it Chi} \left( z \right) 
+{\it \_C3}\,{\it Shi} \left( z \right)</math>
==对称性==
<math>Chi(-z)=Chi(z)</math>
==表示为其他特殊函数==
[[Meijer G函数]]
*<math>     </math>
*<math>\frac{ -1}{2}\,\sqrt {\pi }
G^{2, 0}_{1, 3}\left(-1/4\,{z}^{2}\, \Big\vert\,^{1}_{0, 0, 1/2}\right)
-1/2\,i\pi     </math>
[[超几何函数]]

*<math>Chi(z)=z*_{1}F_{2}(1,1;3/2,2,2; (1/4)*z^2)     </math>

==级数展==
*<math> {\it Chi} \left( z \right) =(\gamma+\ln  \left( z \right) +{\frac {1}{4}}{z}^{2}+{\frac {1}{96}}{z}^{4}+{\frac {1}{4320}}{z}^{6}+{\frac {1}{322560}}{z}^{8}+{\frac {1}{
36288000}}{z}^{10}+{\frac {1}{5748019200}}{z}^{12}+{\frac {1}{
1220496076800}}{z}^{14}+O \left( {z}^{16} \right) )    </math>

==图集==
{|
|[[File:Chi(x) Re complex 3D plot.png|thumb|Chi(x) Re complex 3D plot]]
|[[File:Chi(x) Im complex 3D plot.png|thumb|Chi(x) Im complex 3D plot]]
|[[File:Chi(x) abs complex 3D plot.png|thumb|Chi(x) abs complex 3D plot]]
|}
{|
|[[File:Chi(x) abs complex density plot.JPG|thumb|Chi(x) abs complex density plot]]
|[[File:Chi(x) Re complex density plot.JPG|thumb|Chi(x) Re complex density plot]]
|[[File:Chi(x) Im complex density plot.JPG|thumb|Chi(x) Im complex density plot]]
|
|}
==参见==
*[[Sinhc函数]]
*[[Coshc函数]]
*[[Tanc函数]]
*[[Tanhc函数]]
*[[Shi函数]]

==参考文献==
<references/>

[[Category:特殊函数]]