NAG CL Interfaces18ccc (bessel_​k0_​scaled)

1Purpose

s18ccc returns a value of the scaled modified Bessel function ${e}^{x}{K}_{0}\left(x\right)$.

2Specification

 #include
 double s18ccc (double x, NagError *fail)
The function may be called by the names: s18ccc, nag_specfun_bessel_k0_scaled or nag_bessel_k0_scaled.

3Description

s18ccc evaluates an approximation to ${e}^{x}{K}_{0}\left(x\right)$, where ${K}_{0}$ is a modified Bessel function of the second kind. The scaling factor ${e}^{x}$ removes most of the variation in ${K}_{0}\left(x\right)$.
The function uses the same Chebyshev expansions as s18acc, which returns the unscaled value of ${K}_{0}\left(x\right)$.

4References

NIST Digital Library of Mathematical Functions

5Arguments

1: $\mathbf{x}$double Input
On entry: the argument $x$ of the function.
Constraint: ${\mathbf{x}}>0.0$.
2: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_ARG_LE
On entry, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}>0.0$.

7Accuracy

Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

8Parallelism and Performance

s18ccc is not threaded in any implementation.

None.

10Example

This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.

10.1Program Text

Program Text (s18ccce.c)

10.2Program Data

Program Data (s18ccce.d)

10.3Program Results

Program Results (s18ccce.r)