gives the Dawson integral .
- 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.
Examplesopen allclose all
Basic 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:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
Specific Values (3)
Simple exact values are generated automatically:
Limiting values at infinity:
Find positive maximum of DawsonF[x]:
Function Properties (5)
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:
First derivative with respect to z:
Higher derivatives with respect to z:
Plot the higher derivatives with respect to z:
Formula for the derivative with respect to :
Compute the indefinite integral using Integrate:
Verify the anti-derivative:
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:
Find series expansion for an arbitrary symbolic direction :
Taylor expansion at a generic point:
Generalizations & Extensions (2)
DawsonF can be applied to a power series:
Infinite arguments give symbolic results:
Find the value and position of the maximum of the Dawson function:
Express a probability density function in terms of the Dawson function:
Properties & Relations (1)