NAG CL Interface
s18cdc (bessel_​k1_​scaled)

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1 Purpose

s18cdc returns a value of the scaled modified Bessel function exK1(x).

2 Specification

#include <nag.h>
double  s18cdc (double x, NagError *fail)
The function may be called by the names: s18cdc, nag_specfun_bessel_k1_scaled or nag_bessel_k1_scaled.

3 Description

s18cdc 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 function uses the same Chebyshev expansions as s18adc, which returns the unscaled value of K1(x).

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

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

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
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.
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.

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.
s18cdc 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 (s18cdce.c)

10.2 Program Data

Program Data (s18cdce.d)

10.3 Program Results

Program Results (s18cdce.r)