The **Struve function** is an uncommon special function defined by:

Where:

- v = the order of the Struve function,
- Γ = the gamma function.

While the function definition might seem a little complicated, you’ll rarely have to solve it. Most popular mathematical software includes it as a built in function. For example, in Maple, the function is **StruveH.** There are a few online calculators, including this one that calculates the modified Struve function, L_{v}(x).

## Notation for the Struve Function

The **Struve function** is generally denoted by H_{v}(x) or H_{n}(x). Occasionally you may see the “H” bolded (**H**_{v}(x)) or in lowercase h_{v}(x), sometimes to distinguish it from Hermite polynomials. The modified Struve is usually denoted with an L instead of H.

## Use as Solutions to Bessel Differential Equations

Developed by H. Struve in 1882, the function is a solution to the non-homogeneous (or *inhomogeneous*) Bessel differential equation. Two versions of the function exist; Each version solves a different form of the inhomogenous Bessel equation:

Struve functions are generalized by the hypergeometric and Meijer G functions.

## Uses

The Struve function can be used for various calculations in mathematical physics. For example, to describe thin disk vibration and for various purposes in the theory of electromagnetism.

## References

Luke, Y. (1969). Special Functions and Their Approximations:, Volume 2. Academic Press.

Maplesoft. StruveH, StruveL. Retrieved December 2, 2019 from: https://www.maplesoft.com/support/help/Maple/view.aspx?path=StruveH

Oldham, K. et al. (2010). An Atlas of Functions: with Equator, the Atlas Function Calculator. Springer Science and Business Media.

Rojas, S. et al. (2015). Learning SciPy for Numerical and Scientific Computing – Second Edition. Packt Publishing Ltd.

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