Subsequent subsections treat the computation of Struve functions. The treatment
of Lommel and Anger–Weber functions is similar. For a review of methods for the computation of 
see Zanovello (1975).
Although the power-series expansions (11.2.1) and (11.2.2),
and the Bessel-function expansions of §11.4(iv) converge for all
finite values of 
, they are cumbersome to use when 
is large owing to
slowness of convergence and cancellation. For large and/or 
the
asymptotic expansions given in §11.6 should be used instead.
For numerical purposes the most convenient of the representations given in
§11.5, at least for real variables, include the integrals
(11.5.2)–(11.5.5) for 
and
. Subsequently and 
are obtainable via (11.2.5) and (11.2.6). Other integrals
that appear in §11.5(i) have highly oscillatory integrands unless
is small.
A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. To insure stability the integration path must be chosen so that as we proceed along it the wanted solution grows in magnitude at least as rapidly as the complementary solutions.
Suppose 
and 
is real and positive. Then from the limiting forms
for small argument (§§11.2(i), 10.7(i),
10.30(i)), limiting forms for large argument
(§§11.6(i), 10.7(ii), 10.30(ii)), and the
connection formulas (11.2.5) and (11.2.6), it is seen that
and 
can be computed in a stable manner
by integrating forwards, that is, from the origin toward infinity. The solution
needs to be integrated backwards for small , and either
forwards or backwards for large depending whether or not 
exceeds
. For 
both forward and backward integration
are unstable, and boundary-value methods are required (§3.7(iii)).
Sequences of values of and , with
fixed, can be computed by application of the inhomogeneous difference equations
(11.4.23) and (11.4.25). There are similar problems to those
described in §11.13(iv) concerning stability. In consequence
forward recurrence, backward recurrence, or boundary-value methods may be
necessary. See §3.6 for implementation of these methods, and with
the Weber function 
as an example.
