NAG FL Interface
s18cdf (bessel_​k1_​scaled)

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1 Purpose

s18cdf returns a value of the scaled modified Bessel function exK1(x) via the function name.

2 Specification

Fortran Interface
Function s18cdf ( x, ifail)
Real (Kind=nag_wp) :: s18cdf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  s18cdf_ (const double *x, Integer *ifail)
The routine may be called by the names s18cdf or nagf_specfun_bessel_k1_scaled.

3 Description

s18cdf evaluates an approximation to exK1(x), where K1 is a modified Bessel function of the second kind. The scaling factor ex removes most of the variation in K1(x).
The routine uses the same Chebyshev expansions as s18adf, which returns the unscaled value of K1(x).

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument x of the function.
Constraint: x>0.0.
2: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, x=value.
Constraint: x>0.0.
K1 is undefined and the function returns zero.
On entry, x=value.
Constraint: x>value.
The function returns the value of the function at the smallest permitted value of the argument.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

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.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s18cdf is not threaded in any implementation.

9 Further Comments


10 Example

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

10.1 Program Text

Program Text (s18cdfe.f90)

10.2 Program Data

Program Data (s18cdfe.d)

10.3 Program Results

Program Results (s18cdfe.r)