nag_bessel_k_alpha_scaled (s18ehc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_bessel_k_alpha_scaled (s18ehc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_bessel_k_alpha_scaled (s18ehc) returns a sequence of values for the scaled modified Bessel functions e x K α+n x  for real x>0 , selected values of α0  and n = 0 , 1 , , N .

2  Specification

#include <nag.h>
#include <nags.h>
void  nag_bessel_k_alpha_scaled (double x, Integer ia, Integer ja, Integer nl, double b[], NagError *fail)

3  Description

nag_bessel_k_alpha_scaled (s18ehc) evaluates a sequence of values for the scaled modified Bessel function of the second kind e x K α x , where x  is real and non-negative and α 0, 1 2 , 1 3 , 1 4 , 2 3 , 3 4  is the order. The N+1 -member sequence is generated for orders α , α + 1 , , α + N .

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5  Arguments

1:     xdoubleInput
On entry: the argument x  of the function.
Constraint: x>0.0 .
2:     iaIntegerInput
3:     jaIntegerInput
On entry: the numerator i  and denominator j , respectively, of the order α = i / j  of the first member in the required sequence of function values. Only the following combinations of pairs of values of i  and j  are allowed:
  • i=0  and j=1  corresponds to α=0 ;
  • i=1  and j=2  corresponds to α = 1 2 ;
  • i=1  and j=3  corresponds to α = 1 3 ;
  • i=1  and j=4  corresponds to α = 1 4 ;
  • i=2  and j=3  corresponds to α = 2 3 ;
  • i=3  and j=4  corresponds to α = 3 4 .
Constraint: ia and ja must constitute a valid pair ia,ja = 0,1 , 1,2 , 1,3 , 1,4 , 2,3  or 3,4 .
4:     nlIntegerInput
On entry: the value of N . Note that the order of the last member in the required sequence of function values is given by α+N .
Constraint: 0 nl 100 .
5:     b[nl+1]doubleOutput
On exit: with fail.code=NE_NOERROR  or fail.code=NW_SOME_PRECISION_LOSS , the required sequence of function values: b n  contains K α+n x , for n = 0 , 1 , , N .
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_INT
On entry, nl=value .
Constraint: 0 nl 100 .
NE_INT_2
On entry, ia=value , ja=value .
Constraint: ia and ja must constitute a valid pair (ia,ja).
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.
NE_OVERFLOW_LIKELY
The evaluation has been abandoned due to the likelihood of overflow.
NE_REAL
On entry, x=value .
Constraint: x>0.0 .
NE_TERMINATION_FAILURE
The evaluation has been abandoned due to failure to satisfy the termination condition.
NE_TOTAL_PRECISION_LOSS
The evaluation has been abandoned due to total loss of precision.
NW_SOME_PRECISION_LOSS
The evaluation has been completed but some precision has been lost.

7  Accuracy

All constants in the underlying function are specified to approximately 18 digits of precision. If t  denotes the number of digits of precision in the floating point arithmetic being used, then clearly the maximum number of correct digits in the results obtained is limited by p = mint,18 . Because of errors in argument reduction when computing elementary functions inside the underlying function, the actual number of correct digits is limited, in general, by p-s , where s max1, log 10 x  represents the number of digits lost due to the argument reduction. Thus the larger the value of x , the less the precision in the result.

8  Further Comments

None.

9  Example

The example program evaluates e x K 0 x , e x K 1 x , e x K 2 x  and e x K 3 x  at x=0.5 , and prints the results.

9.1  Program Text

Program Text (s18ehce.c)

9.2  Program Data

Program Data (s18ehce.d)

9.3  Program Results

Program Results (s18ehce.r)


nag_bessel_k_alpha_scaled (s18ehc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012