Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

Limiting value at infinity:

Values at zero:

WeberE for symbolic ν and x:

Find the first positive maximum of WeberE:

WeberE defined as StruveH for integer orders:

Evaluate WeberE for half-integer orders:

Plot the WeberE function for integer () and half-integer () orders:

Plot the real part of :

Plot the imaginary part of :

Plot the real part of :

Plot the imaginary part of :

The real domain of :

The complex domain of :

is defined for all real values:

The complex domain is the whole plane:

The approximate function range of :

Use FullSimplify to simplify Weber functions:

WeberE threads elementwise over lists:

is an analytic function of x:

is neither non-decreasing nor non-increasing:

is not injective:

is neither non-negative nor non-positive:

has neither singularities nor discontinuities:

is neither convex nor concave:

TraditionalForm formatting:

The first derivatives with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z when ν=1/4:

The formula for the derivative with respect to z when ν=2:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The general term in the series expansion using SeriesCoefficient:

The Taylor expansion at a generic point: