naginterfaces.library.specfun.struve_​i1ml1

naginterfaces.library.specfun.struve_i1ml1(x)

struve_i1ml1 returns the value of $I_1\left(x\right)-L_1\left(x\right)$ where $I_1\left(x\right)$ is the modified Bessel function of the first kind of order $1$, and $L_1\left(x\right)$ is the modified Struve function of order $1$.

For full information please refer to the NAG Library document for s18gd

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/s/s18gdf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

iml1float

The value of the function at $x$.

Raises

NagValueError

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $x\ge 0.0$.

Notes

struve_i1ml1 evaluates an approximation to $I_1\left(x\right)-L_1\left(x\right)$.

Please consult the NIST Digital Library of Mathematical Functions for a detailed discussion of the Struve function including special cases, transformations, relations and asymptotic approximations.

The approximation method used by this function is based on Chebyshev expansions.

References

NIST Digital Library of Mathematical Functions

MacLeod, A J, 1996, MISCFUN, a software package to compute uncommon special functions, ACM Trans. Math. Software (TOMS) (22(3)), 288–301