Defining a spherical Struve function
we show that the Struve transform of half integer order, or spherical Struve transform,
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0334270000003994/resource/name/S0334270000003994_eqnU1.gif?pub-status=live)
where n is a non-negative integer, may under suitable conditions be solved for f(t):
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0334270000003994/resource/name/S0334270000003994_eqnU2.gif?pub-status=live)
where
is the sum of the first n + 1 terms in the asymptotic expansion of φn(x) as x → ∞. The coefficients in the asymptotic expansion are identified as
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0334270000003994/resource/name/S0334270000003994_eqnU3.gif?pub-status=live)
It is further shown that functions φn (x) which are representable as spherical Struve transforms satisfy n + 1 integral constraints, which in turn allow the construction of many equivalent inversion formulae.