Struve function
In mathematics, Struve functions Hα(x), are solutions y(x) of the non-homogeneous Bessel's differential equation:
introduced by Hermann Struve (1882). The complex number α is the order of the Struve function, and is often an integer. The modified Struve functions Lα(x) are equal to −ie− iαπ/2Hα(ix).
Since this is a non-homogeneous equation, solutions can be constructed from a single particular solution by adding the solutions of the homogeneous problem. In this case, the homogeneous solutions are the Bessel functions, and the particular solution may be chosen as the corresponding Struve function.
Struve functions, denoted as Hα(x) have the following power series form
where Γ(z) is the gamma function.
The modified Struve function, denoted as Lν(z) have the following power series form
Another definition of the Struve function, for values of α satisfying Re(α) > − 1/2, is possible using an integral representation:
For small x, the power series expansion is given above.
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