DawsonF
![TemplateBox[{z}, DawsonF]](Files/DawsonF.zh/5.png "TemplateBox[{z}, DawsonF]"){kind=small}
DawsonF
DawsonF[z]
给出 Dawson 积分 ![TemplateBox[{z}, DawsonF]](Files/DawsonF.zh/1.png "TemplateBox[{z}, DawsonF]"){kind=small}
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![TemplateBox[{z}, DawsonF]=e^(-z^2) int_0^ze^(t^2)dt](Files/DawsonF.zh/2.png "TemplateBox[{z}, DawsonF]=e^(-z^2) int_0^ze^(t^2)dt"){kind=small}
范例
打开所有单元 关闭所有单元基本范例 (5)
DawsonF[2.5]Plot[DawsonF[x], {x, -10, 10}]ComplexPlot3D[DawsonF[z], {z, -2 - 2I, 2 + 2I}, PlotLegends -> Automatic]Series[DawsonF[x], {x, 0, 10}]Infinity 处的渐近展开式：
Series[DawsonF[x], {x, ∞, 5}]//Normal//FullSimplify范围 (33)
数值计算 (6)
N[DawsonF[1 / E]]DawsonF[-.46]N[DawsonF[4 / 3], 50]DawsonF[1.11111111111111111111111]N[DawsonF[I Pi + 5]]DawsonF[.9`100]//TimingDawsonF[58.`10000];//Timing用 Interval 和 CenteredInterval 对象计算最坏情况下的区间：
DawsonF[Interval[{0.5, 0.6}]]DawsonF[CenteredInterval[1 / 2, 1 / 100]]或用 Around 计算一般情况下的统计区间：
DawsonF[ Around[2.1, 0.01]]DawsonF[{{1.2, 0}, {0, -1.2}}]或用 MatrixFunction 计算矩阵形式的 DawsonF 函数：
MatrixFunction[DawsonF, {{1.2, 0}, {0, -1.2}}]特殊值 (3)
DawsonF[0]{Limit[DawsonF[x], x -> Infinity], Limit[DawsonF[x], x -> -Infinity]}求 DawsonF[x] 的正极大值：
xmax = x /. FindRoot[D[DawsonF[x ], x] == 0, {x, 1}]Plot[DawsonF[x ], {x, -5, 5}, Epilog -> Style[Point[{xmax, DawsonF[xmax ]}], PointSize[Large], Red]]可视化 (2)
函数属性 (11)
DawsonF 对所有实数和复数都有定义：
FunctionDomain[DawsonF[x], x]FunctionDomain[DawsonF[z], z, Complexes]DawsonF 的近似值域：
FunctionRange[DawsonF[x], x, y]//QuietDawsonF 是奇函数：
DawsonF[-x]DawsonF 具有镜像属性 ![TemplateBox[{{z, }}, DawsonF]=TemplateBox[{z}, DawsonF]](Files/DawsonF.zh/3.png "TemplateBox[{{z, }}, DawsonF]=TemplateBox[{z}, DawsonF]"){kind=small}
：
FullSimplify[DawsonF[Conjugate[z]] == Conjugate[DawsonF[z]]]DawsonF 逐项作用于列表的各个元素
DawsonF[{1.0, 2.0, 3.0, 4.0, 5.0}]DawsonF 是 x 的解析函数：
FunctionAnalytic[DawsonF[x], x]FunctionSingularities[DawsonF[x], x]//QuietFunctionDiscontinuities[DawsonF[x], x]//QuietDawsonF 既不是非递增，也不是非递减：
FunctionMonotonicity[DawsonF[x], x]DawsonF 不是单射函数：
FunctionInjective[DawsonF[x], x]Plot[{DawsonF[x], .2}, {x, -10, 10}]DawsonF 不是满射函数：
FunctionSurjective[DawsonF[x], x]Plot[{DawsonF[x], -1}, {x, -10, 10}]DawsonF 既不是非负，也不是非正：
FunctionSign[DawsonF[x], x]DawsonF 既不凸，也不凹：
FunctionConvexity[DawsonF[x], x]微分 (3)
D[DawsonF[z], z]Table[D[DawsonF[z], {z, k}], {k, 1, 3}]//FullSimplifyPlot[%, {z, -4, 4}, PlotLegends -> {"First Derivative", "Second Derivative", "Third Derivative"}]
D[DawsonF[z], {z, k}]// FullSimplify积分 (3)
用 Integrate 计算不定积分：
Integrate[DawsonF[x], x]// FullSimplifyFullSimplify[D[%, x]]// FullSimplifyIntegrate[DawsonF[x], {x, 0, 15}]Integrate[DawsonF[x] x ^ a, x]// FullSimplifyIntegrate[DawsonF[x + a] x, x]// FullSimplify级数展开 (5)
用 Series 求泰勒展开式：
Series[DawsonF[x], {x, 0, 10}]
terms = Normal@Table[Series[DawsonF[x], {x, 0, m}], {m, 1, 5, 2}];
Plot[{DawsonF[x], terms}, {x, -5, 5}, PlotRange -> {-10, 10}]用 SeriesCoefficient 获取级数展开式的通项:
SeriesCoefficient[DawsonF[x], {x, 1, n}]求 Infinity 处的级数展开式：
Series[DawsonF[x], {x, Infinity, 1}]
Series[DawsonF[x], {x, DirectedInfinity[z], 1}, Assumptions -> x > 0]// FullSimplifySeries[DawsonF[x], {x, x0, 2}]// FullSimplify推广和延伸 (2)
可将 DawsonF 应用于幂级数：
DawsonF[ Log[1 + x] + O[x] ^ 10]DawsonF[{-Infinity, Infinity, I Infinity, -I Infinity}]应用 (3)
FindMaximum[DawsonF[x], {x, 1}]𝒟 = TransformedDistribution[u ^ 2 + 3v, {u, v} ProductDistribution[{ExponentialDistribution[3], 2}]];PDF[𝒟, x]DawsonF 出现在截断高斯函数的傅立叶变换中：
ft = FourierTransform[Exp[-x^2]UnitStep[x], x, ω]ComplexPlot3D[Evaluate[ft], {ω, -10 - 10I, 10 + 0I}, ScalingFunctions -> "Log"]属性和关系 (1)
使用 FunctionExpand 将 DawsonF 展开为虚数误差函数的形式：
FunctionExpand[DawsonF[x]]
Wolfram Research (2008)，DawsonF，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DawsonF.html.
文本
Wolfram Research (2008)，DawsonF，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DawsonF.html.
CMS
Wolfram 语言. 2008. "DawsonF." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/DawsonF.html.
APA
Wolfram 语言. (2008). DawsonF. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/DawsonF.html 年