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For real values of parameter  and positive argument  , the values of the Struve functions  and  are real.
The Struve functions  and  have rather simple values for the argument  :
In the cases when parameter  is equal to  , the Struve functions  and  can be expressed through the sine and cosine (or hyperbolic sine and cosine) multiplied by rational and sqrt functions, for example:
The previous formulas are the particular cases of the following general formulas:
The Struve functions  and  are defined for all complex values of their parameter  and variable  . They are analytical functions of  and  over the whole complex  ‐ and  ‐planes excluding the branch cuts. For fixed integer  , the functions  and  are entire functions of  . For fixed  , the functions  and  are entire functions of  .
For fixed  , the functions  and  have an essential singularity at  . At the same time, the point  is a branch point (except cases for integer  ).
With respect to  , the Struve functions have only one essential singular point at  .
For fixed noninteger  , the functions  and  have two branch points:  and  .
If functions  and  have branch cuts, they are single‐valued functions on the  ‐plane cut along the interval  , where they are continuous from above:
From below, functions have discontinuities that are described by the formulas:
The Struve functions  and  do not have periodicity.
The Struve functions  and  have mirror symmetry (except on the branch cut interval (-∞, 0)):
The Struve functions  and  have generalized parity (either odd or even) with respect to variable  :
The Struve functions  and  have the following series expansions through series that converge on the whole  ‐plane:
Interestingly, closed-form expressions for the truncated version of the Taylor series at the origin can be expressed through the generalized hypergeometric function  , for example:
The asymptotic behavior of the Struve functions  and  can be described by the following formulas (only the main terms of asymptotic expansion are given):
The previous formulas are valid in any directions approaching point  to infinity (z∞). In particular cases when  or  , these formulas can be simplified to the following relations:
The Struve functions  and  have simple integral representations through the sine (or hyperbolic sine) and power functions:
Arguments of the Struve functions  and  with square root arguments can sometimes be simplified:
The Struve functions  and  satisfy the following recurrence identities:
The previous identities can be generalized to the following recurrence identities with a jump of length n:
The derivatives of the Struve functions  and  have simple representations that can also be expressed through Struve functions with different indices:
The symbolic  -order derivatives have the following representations:
The Struve functions  and  appeared as special solutions of the special inhomogeneous Bessel second-order linear differential equations:
where  and  are arbitrary constants and  ,  ,  , and  are Bessel functions.
The previous equations are very similar and can be converted into each other by changing  to  .
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