Evaluate numerically to high precision:

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

Evaluate for complex arguments and parameters:

Evaluate StruveL efficiently at high precision:

StruveL threads elementwise over lists:

For half-integer indices, StruveL evaluates to elementary functions:

Value of at a complex infinity is indeterminate:

Limiting value at infinity:

Find a root of :

Plot the StruveL function for integer :

Plot the StruveL function for half-integer values of :

Plot the real part of :

Plot the imaginary part of :

Plot the real part of :

Plot the imaginary part of :

Function domain of StruveL for half-integer :

Complex domain:

Approximate function range of StruveL for half-integer values of :

Parity:

is analytic in the interior of its real domain:

It is not analytic everywhere, as it has both singularities and discontinuities:

is nondecreasing on its real domain:

is injective:

is not surjective:

is non-negative on its real domain:

is convex on its real domain:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Plot higher derivatives for :

Formula for the derivative:

Indefinite integral:

Definite integral:

Definite integral of the odd integrand over an interval centered at the origin is 0:

Definite integral of the even integrand over an interval centered at the origin:

This is twice the integral over half the interval:

Taylor expansion for :

Plot the first three approximations for around :

General term in the series expansion of :

Series expansion of StruveL at infinity:

StruveL can be applied to a power series:

Compute the Laplace transform using LaplaceTransform:

HankelTransform:

Argument simplifications:

Recurrence relation:

Series representation:

Representation in terms of StruveH:

StruveL can be represented in terms of MeijerG:

TraditionalForm formatting: