- #1

coccoinomane

- 19

- 0

Hi everybody!

I kindly request your help. I have to compute functions like

[tex]\frac{ \sin (r x) - r x \cos (r x)}{r^3}[/tex]

(primitive function of x sin(rx) )

or

[tex]\frac{ -r x (120 - 20 r^2 x^2 + r^4 x^4) cos(r x) +

5 (24 - 12 r^2 x^2 + r^4 x^4) \sin(r x)}{r^7}[/tex]

(primitive function of x^5 sin(rx) )

when both r and x varies.

The problem with these functions is that the sin and cos factors are very similar to each other when x approaches zero. This is a big issue: double precision is not enough to compute the difference because of roundoff errors or simply because 14-15 digits are not enough to distinguish the two factors.

I kind of solved the problem for the first function. In fact, I could express it up to a factor as the first order spherical bessel function:

[tex]j1(x) = \frac{\sin(x)/x - \cos(x)}{x}[/tex],

which is well computed in the GNU Scientific Library.

I need to calculate those functions to solve the integral I discussed in https://www.physicsforums.com/showthread.php?p=2028408#post2028408 and that uart helped me to solve.

Thank you very much for any suggestion,

Guido

I kindly request your help. I have to compute functions like

[tex]\frac{ \sin (r x) - r x \cos (r x)}{r^3}[/tex]

(primitive function of x sin(rx) )

or

[tex]\frac{ -r x (120 - 20 r^2 x^2 + r^4 x^4) cos(r x) +

5 (24 - 12 r^2 x^2 + r^4 x^4) \sin(r x)}{r^7}[/tex]

(primitive function of x^5 sin(rx) )

when both r and x varies.

The problem with these functions is that the sin and cos factors are very similar to each other when x approaches zero. This is a big issue: double precision is not enough to compute the difference because of roundoff errors or simply because 14-15 digits are not enough to distinguish the two factors.

I kind of solved the problem for the first function. In fact, I could express it up to a factor as the first order spherical bessel function:

[tex]j1(x) = \frac{\sin(x)/x - \cos(x)}{x}[/tex],

which is well computed in the GNU Scientific Library.

I need to calculate those functions to solve the integral I discussed in https://www.physicsforums.com/showthread.php?p=2028408#post2028408 and that uart helped me to solve.

Thank you very much for any suggestion,

Guido

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