DawsonF
DawsonF[z]
gives the Dawson integral .
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Dawson integral is defined by .
- For certain special arguments, DawsonF automatically evaluates to exact values.
- DawsonF can be numerically evaluated to arbitrary numerical precision.
- DawsonF automatically threads over lists.
- DawsonF can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Asymptotic expansion at Infinity:
Scope (33)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:
Or compute average-case statistical intervals using Around:
Compute the elementwise values of an array:
Or compute the matrix DawsonF function using MatrixFunction:
Specific Values (3)
Simple exact values are generated automatically:
Find positive maximum of DawsonF[x]:
Visualization (2)
Function Properties (11)
DawsonF is defined for all real and complex values:
Approximate function range for DawsonF:
DawsonF is an odd function:
DawsonF has the mirror property :
DawsonF threads elementwise over lists:
DawsonF is an analytic function of x:
Has no singularities or discontinuities:
DawsonF is neither nondecreasing nor nonincreasing:
DawsonF is not injective:
DawsonF is not surjective:
DawsonF is neither non-negative nor non-positive:
DawsonF is neither convex nor concave:
Differentiation (3)
Integration (3)
Compute the indefinite integral using Integrate:
Series Expansions (5)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
Find the series expansion at Infinity:
Generalizations & Extensions (2)
Applications (3)
Find the value and position of the maximum of the Dawson function:
Express a probability density function in terms of the Dawson function:
DawsonF appears in the Fourier transform of truncated Gaussians:
Properties & Relations (1)
Use FunctionExpand to expand DawsonF in terms of the imaginary error function:
Text
Wolfram Research (2008), DawsonF, Wolfram Language function, https://reference.wolfram.com/language/ref/DawsonF.html.
CMS
Wolfram Language. 2008. "DawsonF." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DawsonF.html.
APA
Wolfram Language. (2008). DawsonF. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DawsonF.html