whittaker Module Reference

Calculates special integrals. More...

Functions/Subroutines
subroutine, public	whittaker_c0a (wc, r, expa, erfa, alpha, l1, l2, n)
	int(y^(2+l1+l2) * exp(-alpha*y*y),y=0..x) / x^(l2+1); wc(:) :: output r(:) :: coordinate expa(:) :: exp(-alpha*r(:)**2) erfa(:) :: erf(sqrt(alpha)*r(:)) alpha :: exponent l1, l2 :: L-quantum number n :: number of points
subroutine, public	whittaker_ci (wc, r, expa, alpha, l, n)
	int(y^(l+1) * exp(-alpha*y*y),y=x..infinity);

Variables
real(kind=dp), parameter	epsilon = 1.e-2_dp

Detailed Description

Calculates special integrals.

Author

JGH 10-08-2004

Function/Subroutine Documentation

whittaker_c0a()

subroutine, public whittaker::whittaker_c0a	(	real(kind=dp), dimension(n), intent(out)	wc,
		real(kind=dp), dimension(n), intent(in)	r,
		real(kind=dp), dimension(n), intent(in)	expa,
		real(kind=dp), dimension(n), intent(in)	erfa,
		real(kind=dp), intent(in)	alpha,
		integer, intent(in)	l1,
		integer, intent(in)	l2,
		integer, intent(in)	n
	)

int(y^(2+l1+l2) * exp(-alpha*y*y),y=0..x) / x^(l2+1); wc(:) :: output r(:) :: coordinate expa(:) :: exp(-alpha*r(:)**2) erfa(:) :: erf(sqrt(alpha)*r(:)) alpha :: exponent l1, l2 :: L-quantum number n :: number of points

Parameters

wc	...
r	...
expa	...
erfa	...
alpha	...
l1	...
l2	...
n	...

Author

JGH 10-08-2004

Definition at line 51 of file whittaker.F.

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whittaker_ci()

subroutine, public whittaker::whittaker_ci	(	real(kind=dp), dimension(n), intent(out)	wc,
		real(kind=dp), dimension(n), intent(in)	r,
		real(kind=dp), dimension(n), intent(in)	expa,
		real(kind=dp), intent(in)	alpha,
		integer, intent(in)	l,
		integer, intent(in)	n
	)

int(y^(l+1) * exp(-alpha*y*y),y=x..infinity);

             (-1 - 1/2 l~)                          2
     1/2 alpha              GAMMA(1/2 l + 1, alpha x )


   wc(:)    :: output
   r(:)     :: coordinate
   expa(:)  :: exp(-alpha*r(:)**2)
   alpha    :: exponent
   l        :: L-quantum number
   n        :: number of points

Parameters

wc	...
r	...
expa	...
alpha	...
l	...
n	...

Author

JGH 10-08-2004

Definition at line 339 of file whittaker.F.

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Variable Documentation

epsilon

real(kind=dp), parameter whittaker::epsilon = 1.e-2_dp

Definition at line 23 of file whittaker.F.